Robert Lanier Tate III, Deborah Ann Tate Lewis, and Mary Denise Tate Spires (hereinafter referred to collectively as “the heirs”) appeal from a summary judgment entered by the Calhoun Circuit Court (“the trial court”) in favor of the Water Works and Sewer Board of the City of Oxford (“the Board”) on the heirs’ claims against the Board, and on some of the Board’s claims against the heirs, regarding a parcel of real property in Calhoun County (“the disputed property”). We affirm the trial court’s judgment.
Facts and Procedural History
The following facts are undisputed. Robert L. Tate, Jr. (“Robert”), died intestate on December 24, 1972, and he was survived by his wife, Mary Bernice Ginn Tate (“the widow”), and the hems, who were minors at the time of Robert’s death. *909Before Robert’s death, Robert and the widow owned, as joint tenants with a right of survivorship, a parcel of property on Ingram Street in Oxford, where the family resided (“the home property”). The widow claimed the home property as her homestead following Robert’s death. Robert also owned, at the time of his death and in his name alone, property located west of Stephens Avenue in Oxford (“the Stephens Avenue property”); the Stephens Avenue property had been conveyed to Robert under three separate deeds. The disputed property is an approximately 2.3-acre portion of the Stephens Avenue property. The widow never sought to administer Robert’s estate, and she never claimed or asserted her dower rights or any other rights of a widow with regard to the Stephens Avenue property.
In 1987, the Board began making plans to acquire a site upon which to build a water tower to service the water needs of the citizens of Oxford, and, having determined that the disputed property was an appropriate location, the Board filed a condemnation proceeding in the Calhoun Probate Court against the widow, seeking to condemn the disputed property. The probate court entered an order of condemnation of the disputed property in favor of the Board on December 4, 1987. The Board filed a notice of appeal from that order, disputing the amount it had been ordered to pay for the property; however, after the notice of appeal was filed, the Board entered into a settlement with the widow, and, on June 23, 1988, the widow executed a deed purporting to convey the disputed property to the Board. Construction of the water tower was completed in approximately February 1989, at which time the Board erected a fence along the boundaries of the disputed property; the fence remains in the same location where it was originally erected. The widow died in October 2012.
The heirs filed a complaint against the Board on July 15, 2014, seeking to quiet title to the disputed property; they also sought injunctive relief and a judgment declaring that they own the disputed property in fee simple and that the Board has no interest in the property. The heirs also asserted claims of ejectment and trespass against the Board. The Board filed an answer, which included a number of affirmative defenses, and it counterclaimed against the heirs. The Board contended, among other things, that it owned the disputed property by virtue of statutory adverse possession and/or adverse possession by prescription, and it sought to quiet title to the disputed property and a judgment declaring that the Board owns the disputed property. The heirs filed a reply to the Board’s counterclaim and later amended their complaint, asserting additional claims of inverse condemnation and unjust enrichment against the Board. The heirs and the Board filed competing summary-judgment motions, and, on October 2, 2015, the trial court entered a summary judgment in favor of the Board on the heirs’ claims; quieted title to the disputed property “in the exclusive fee simple ownership of the Board”; enjoined the heirs from obstructing and/or interfering with the Board’s quiet enjoyment and property rights in the disputed property; and dismissed without prejudice the remainder of the Board’s claims against the heirs. The heirs timely appealed to the Alabama Supreme Court; that court transferred the appeal to this court, pursuant to Ala. Code 1975, § 12-2-7(6).
Standard of Review
[1-4] “Our standard of review is straightforward when, as here, the facts are undisputed:
“‘An order granting or denying a summary judgment is reviewed de novo, applying the same standard as the trial *910court applied. American Gen. Life & Accident Ins. Co. v. Underwood, 886 So.2d 807, 811 (Ala.2004). In addition, “[t]his court reviews de novo a trial court’s interpretation of a statute, because only a question of law is presented.” Scott Bridge Co. v. Wright, 883 So.2d 1221, 1223 (Ala.2003). Where, as here, the facts of a case are essentially undisputed, this Court must determine whether the trial court misapplied the law to the undisputed facts, applying a de novo standard of review. Carter v. City of Haleyville, 669 So.2d 812, 816 (Ala.1995). Here, in reviewing the [entry] of a summary judgment when the facts are undisputed, we review de novo the trial court’s interpretation of statutory language and our previous caselaw on a controlling question of law.’ ”
McKinney v. Nationwide Mut. Fire Ins. Co., 33 So.3d 1203, 1206-07 (Ala.2009) (quoting Continental Nat’l Indem. Co. v. Fields, 926 So.2d 1033, 1034-35 (Ala.2005)).
Discussion
The trial court issued a 37-page judgment in this case, in which it determined, among other things, that the Board had acquired title to the disputed property by statutory adverse possession and/or adverse possession by prescription; that the rights of dower, quarantine, and homestead with regard to the widow’s purported interest in the disputed property were inapplicable; and that the heirs had failed to prove the elements of their claims of inverse condemnation and unjust enrichment. The heirs dispute each of those findings on appeal.
The heirs first argue that the Board, as a governmental entity, could not have acquired the disputed property by adverse possession after having secured a deed from the widow.
“Alabama recognizes two types of adverse possession: (1) statutory adverse possession pursuant to § 6-5-200, Ala. Code 1975, and (2) adverse possession by prescription. Sparks v. Byrd, 562 So.2d 211 (Ala.1990). Specifically,
“ ‘ “[a]dverse possession by prescription requires actual, exclusive, open, notorious and hostile possession under a claim of right for a period of twenty years. See, Fitts v. Alexander, 277 Ala. 372, 170 So.2d 808 (1965). Statutory adverse possession requires the same elements, but the statute provides further that if the adverse possessor holds under color of title, has paid taxes for ten years, or derives his title by descent cast or devise from a possessor, he may acquire title in ten years, as opposed to the twenty years required for adverse possession by prescription. [Ala.] Code 1975, § 6-5-200. See, Long v. Ladd, 273 Ala. 410, 142 So.2d 660 (1962).” ’
“562 So.2d at 214 (quoting Kerlin v. Tensaw Land & Timber Co., 390 So.2d 616, 618 (Ala.1980) (emphasis omitted)).”
Henderson v. Dunn, 871 So.2d 807, 810 (Ala.Civ.App.2001).
Specifically, the heirs assert that, following Robert’s death, the widow inherited a life estate in the disputed property and that, as a result, the deed purporting to convey the disputed property to the Board granted only the widow’s life-estate interest in the disputed property to the Board. Thus, the heirs claim, the Board’s use of the disputed property was permissive based on the widow’s deed granting the Board use of the property and, as a result, the prescriptive period did not begin to run until the widow’s death in October 2012. We conclude, however, as explained further below, that the widow did not have a life estate in the disputed property.
At the time of Robert’s death, the real estate of a man dying intestate descended first to any children of the *911intestate in equal parts in fee simple, subject to the widow’s dower and homestead rights. See Title 16, § 1, Ala.Code 1940 (Recomp.1958), Mitchell v. Mitchell, 278 Ala. 670, 671, 180 So.2d 266, 267 (1965), and Loeb v. Callaway, 250 Ala. 524, 526, 35 So.2d 198, 200 (1948). The heirs first argue that the widow inherited a life estate in the disputed property pursuant to her right to claim it in lieu of a homestead. “The homestead rights of a widow and minor children are determined by the law in force at the time of the decedent’s death.” Stroud v. Stroud, 505 So.2d 1209, 1210 (Ala.1987). In Mordecai v. Scott, 294 Ala. 626, 629-30, 320 So.2d 642, 644-45 (1975), our supreme court discussed the law regarding homestead rights applicable at the time of Robert’s death:
“In general, the homestead law provides to named survivors a homestead not exceeding 160 acres in area which is exempt from administration and the payment of debts. Title 7, Sections 661, 663, 697, Code of Alabama, 1940 (Recompiled 1958). Although the term ‘homestead’ is not defined in the statute, this court has stated that ‘[a] homestead, in law, means a home place, or place of the home, and is designed as a shelter of the homestead roof, and not as a mere investment in real estate, or the rents and profits derived therefrom.’ Griffin v. Ayers, 231 Ala. 493, 496, 165 So. 593, 595 (1936). It has been further defined as ‘the roof that shelters and the land used in connection therewith for the comfort and sustenance of the family....’ Moseley v. Neville, 221 Ala. 429, 431, 129 So. 12, 14 (1930), quoted in Griffin v. Ayers, supra. Normally the land must have been occupied by decedent prior to his death. Turner v. Turner, 107 Ala. 465, 18 So. 210 (1895). Contiguous real estate used for rental or commercial purposes and not used by the homeowner or his family is not within the ‘homestead.’ Griffin v. Ayers, supra; Turner v. Turner, supra. But see Cade v. Graffo, 227 Ala. 11, 148 So. 591 (1933), where contiguous property rented to others was determined to be part of the homestead because it was also used by the owner in connection with the homeplace.
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“If the decedent owned no homestead or if the homestead cannot be reduced to statutory value, the widow and minor children may receive an exemption in lieu of homestead in decedent’s other lands. Title 7, Section 662, Code of Alabama, 1940 (Recompiled 1958).”
In the present case, at the time of Robert’s death, Robert, the widow, and the heirs resided on the home property. Because the home property was owned by Robert and the widow jointly with the right of survivorship, the home property vested in the widow as the sole owner at the time of Robert’s death. As a result, the home property never devolved into Robert’s estate. The widow thereafter claimed the home property as her homestead and, thus, could not claim a homestead exemption in any property owned solely by Robert at the time of his death. See Ala.Code 1940 (Recomp.1958), Tit. 47, § 19; and Skipworth v. Skipworth, 383 So.2d 524, 527 (Ala.1980) (concluding that, when the family had resided on property belonging to the widow at the time of her husband’s death, the widow was not entitled to a homestead exemption in the other property of her husband).
The only property owned solely by Robert at the time of his death was the Stephens Avenue property. The heirs argue that the widow could have claimed an “exemption in lieu of homestead” with regard to the Stephens Avenue property following Robert’s death, pursuant to Ala. Code 1940 (Recomp.1958), Tit. 7, § 662. In Drummond Co. v. Gunter, 588 So.2d *912465, 467 (Ala.Civ.App.1991), this court explained:
“Section 662[ of Title 7, Ala.Code 1940 (Recomp.1958),] provides that, if the decedent had no actual homestead at the time of his death, the widow is then entitled to an ‘exemption in lieu of homestead’ of $6,000 out of other real estate owned by the decedent. However, § 662 expressly conditions the widow’s entitlement to this exemption upon her filing a petition, in the probate court or by bill in equity, ‘before a final distribution of the assets of decedent’s estate has been made.’ ”
It is undisputed that the widow in the present case failed, at any time before her death, to seek, either through a petition filed in probate court or through a bill in equity, to have an exemption in lieu of homestead set aside for her with regard to the Stephens Avenue property. Because the widow failed to comply with the statutory requirements of § 662, the widow never possessed an interest in the Stephens Avenue property pursuant to her right to an exemption in lieu of homestead. See Drummond, supra.
The heirs cite Hicks v. Huggins, 405 So.2d 1324, 1327 (Ala.Civ.App.1981), however, for the proposition that “[t]here is no statute of limitation which prescribes the time within which a widow must present her petition to have the homestead set aside where there has been no administration of decedent’s estate.” It is undisputed that, in the present case, there has been no administration of Robert’s estate. The heirs assert that the widow’s failure to file a petition to set aside her homestead exemption does not change the fact that the Board acquired her rights in the disputed property for the remainder of the widow’s life and that her right to assert an interest in the disputed property in lieu of homestead is what was conveyed to the Board by the widow. The heirs fail, however, to cite any authority indicating that the widow’s right to apply for an exemption in lieu of homestead was an assignable property right. The heirs also fail to cite any authority providing that the specific holding in Hicks v. Huggins—i.e., that there is no statute of limitations within which a widow may apply for her homestead exemption— applies also to exemptions in lieu of homestead. See Sea Calm Shipping Co., S.A. v. Cooks, 565 So.2d 212, 216 (Ala.1990) (“Where an appellant fails to cite any authority for an argument, this Court may affirm the judgment as to those issues, for it is neither this Court’s duty nor its function to perform all the legal research for an appellant.”). Accordingly, we decline to reverse the trial court’s judgment on that basis.
The heirs next argue that Tit. 7, § 663, Ala.Code 1940 (Recomp.1958), applies in the present case such that the widow and the hens each acquired equal interests as tenants in common in the disputed property upon Robert’s death. Section 663 provided, in pertinent part, that “[w]hen the homestead set apart to the widow and minor children, or either, constitutes all the real estate owned in this state by the decedent at the time of his death, whether there be administration on the estate or not and whether the estate be solvent or insolvent, the title to such homestead vests absolutely in the widow, the children (minors and adults) and the descendants of deceased children.” Section 663, “however, works to vest title in the widow, children (minors and adults), and descendants of deceased children absolutely only after the homestead has been set apart by a proceeding in a court of proper jurisdiction.” Rodgers v. Bradley, 533 So.2d 546, 550 (Ala.1988). Because there had been no setting apart of a homestead at any time in the present case, § 663 did not operate to vest title in the *913disputed property in the widow and the heirs. See id.
The heirs next argue on appeal that the widow possessed a life estate in the disputed property based on her dower interest. Section 40 of Title 34, Ala.Code 1940 (Recomp.1958), defined “dower” as “an estate for the life of the widow in a certain portion of,” among other things, “all lands of which the husband was seized in fee during the marriage.” According to Title 34, § 41, Ala. Code 1940 (Recomp.1958), because Robert had “lineal descendants,” the widow’s dower interest was limited to one-third of Robert’s real property. However,
“[a]s pointed out in Gillian v. Gillian, 340 So.2d 785 (Ala.1976), ‘Dower does not vest automatically in the widow but is allocated only on petition of widow, heirs or other interested parties.’ Continuing, the court noted, ‘Dower right is a chose in action or an equity and does not become a property interest until there has been an assignment thereof.’ Gillian v. Gillian, 340 So.2d at 787, 788.”
Land v. Lawyer, 437 So.2d 524, 527 (Ala.1983). In the present case, the widow never petitioned for an allocation of her dower interest in the Stephens Avenue property.
The trial court also determined that, because the widow in the present case failed to file a petition to have her dower interest judicially assigned within 10 years of Robert’s death, the statute of limitations had run. Section 63 of Title 34, Ala.Code 1940 (Recomp.1958), provided:
“All proceedings or suits for dower, when the claim or rights of a voluntary or involuntary alienee of the husband, or any one claiming under such alienee, are involved in such suit or proceedings, must be commenced within three years after the death of the husband, and not after; and in all other cases the proceedings must be commenced within ten years after the death of the husband and not after.”
The heirs argue, however, that the statute of limitations did not bar the widow’s right to dower because, they argue, she remained in possession of the disputed property until she conveyed it to the Board and, they assert, she continued to remain in possession of the disputed property “via her conveyance” to the Board and the Board’s possession thereof until her death in 2012. In Williams v. Anthony, 219 Ala. 98, 99, 121 So. 89, 90 (1929), our supreme court observed that the statute of limitations expressed in § 63 “do[es] not apply to prevent a widow from claiming dower, when she has been in possession of the land since her husband died.” The heirs fail to cite any legal authority indicating that the widow continued to remain in possession of the disputed property by virtue of the Board’s possession following the widow’s purported conveyance of the property to the Board. See Sea Calm Shipping Co., supra. Thus, this court may affirm the trial court’s judgment as to that issue. Moreover, assuming, without deciding, that the widow had remained in possession of the disputed property until the time of her purported conveyance to the Board, we conclude that the widow’s purported conveyance of the disputed property to the Board would have operated to extinguish the widow’s dower right. See Brandon v. Wilkinson, 92 Ala. 530, 530-31, 9 So. 187, 188 (1891); Leddon v. Strickland, 218 Ala. 436, 439, 118 So. 651, 653 (1928); and Aniton v. Robinson, 273 Ala. 76, 84, 134 So.2d 764, 770 (1961). Thus, even assuming that the widow had remained in possession of the disputed property following Robert’s death such that her right to claim a dower interest therein continued beyond the 10-year period set out in § 63, her dower right was extinguished at the time of her purported con*914veyance of the disputed property to the Board on June 23, 1988, and no dower rights remained that could have been assigned to the Board.
The heirs argue on appeal that, “[e]ven if the specific dower interest was not allotted to her during her lifetime, [the widow] could convey her interest in the [disputed property]” to the Board. The heirs assert that, “in some instances, this is referred to as the quarantine or right to quarantine.” Our supreme court, in Marino v. Smith, 454 So.2d 1380, 1382 (Ala.1984), explained the following with regard to quarantine:
“The widow is entitled to quarantine as an incidental right to dower. Hale v. Cox, 240 Ala. 622, 200 So. 772 (1941), The right of quarantine exists before dower is assigned and continues during the widow’s lifetime. Id. Failure to have dower assigned, and permitting the widow to retain possession without more, does not deprive the owner of the fee in the land. Lynch v. Jackson, 235 Ala. 90, 177 So. 347 (1937).”
The right to quarantine allows the widow to “retain possession of the dwelling house where her husband most usually resided next before his death, with the offices and buildings, appurtenant thereto, and the plantation connected therewith, until her dower is assigned her, free from the payment of rent.” Title 34, § 50, Ala.Code 1940 (Recomp.1958).
It is undisputed that Robert’s dwelling house at the time of his death was not located on the disputed property. The heirs argue, however, that the disputed property falls within the definition in § 50 of “the plantation connected therewith” because, they argue, the disputed property was located “only two streets and only a few hundred feet from the dwelling house.” The heirs fail, however, to cite any authority for the proposition that a parcel of property that is not contiguous to, but is in close proximity to, the property containing the dwelling house, even if it had belonged to the decedent at the time of his death, is a part of the “plantation connected” with the dwelling house for purposes of quarantine rights. See id. Regardless, our supreme court has determined that a plantation belonging to the deceased husband located several miles from his residence is not connected to the dwelling house so as to entitle a widow to quarantine rights thereto. See Clary v. Sanders, 43 Ala. 287, 294-95 (1869); and Waters v. Williams, 38 Ala. 680, 683-84 (1863). Additionally, our supreme court confirmed in Hayden v. Robinson, 472 So.2d 606, 609-10 (Ala.1985), that “[t]he failure of the evidence to show conclusively that the second parcel is connected to the first within the meaning of § 50, Title 34, [Ala.Code 1940 (Recomp.1958) ], precludes a determination that [the widow] was entitled to possession of the second parcel under her right to quarantine.” Thus, the heirs failed to show that the widow was entitled to exercise her right to quarantine in the disputed property.
Citing Aniton, supra, the heirs argue that the Board was granted the right to have the widow’s dower interest judicially assigned to it by virtue of the 1988 deed from the widow to the Board and that, as a result, the heirs had no right to possess the disputed property after that interest was transferred and the Board could not adversely possess the disputed property against them until the widow’s death in 2012. We disagree. In Aniton, a widow had purported to convey a portion of her deceased husband’s property to a married couple, although the widow had not yet had any of that property assigned to her by the courts as her dower interest. 273 Ala. at 82, 134 So.2d at 768-69. Our supreme court determined that the married couple had, in equity, a right of action that, when assigned, could give them a life *915estate in at least a part of the tract deeded by the widow and that, as a result, the heirs of the deceased husband could not be said to have a right to possession of the tract as long as the married couple’s right existed. 273 Ala. at 84, 134 So.2d at 771. In Ambon, the purported conveyance to the married couple by the widow occurred within 10 years of the death of the deceased husband. Id. In the present case, however, the widow’s conveyance to the Board occurred outside the 10-year period to claim her dower interest expressed in § 63; thus, any right in the widow to have a dower interest judicially assigned continued only as long as the widow remained in possession of the property. See Williams, supra. We have already determined that the widow’s purported conveyance of the disputed property to the Board extinguished any continuing right held by the widow to have her dower interest judicially assigned and, thus, unlike in Aniton, the widow’s purported conveyance of the disputed property to the Board did not convey to the Board a right in equity to have the widow’s dower interest judicially assigned because any such right was extinguished as a result of that purported conveyance.
In Leddon v. Strickland, 218 Ala. at 439, 118 So. at 653, a widow had failed to have property set aside pursuant to her rights of dower and homestead within the applicable 10-year limitations period. The supreme court explained that she had acquired no title or interest in her deceased husband’s property and could not convey the subject property to those claiming under her deed. Thus, our supreme court determined, those claiming under the widow’s deed purporting to convey the subject property were required to prove ownership of the land by adverse, possession in order to defeat the ownership rights of. the heirs of the widow’s deceased husband. Id. Similarly, in the present case, because the widow’s dower right expired with her purported conveyance of the disputed property to the Board, the Board could establish ownership of the disputed property, as against the heirs, by virtue of adverse possession.
The heirs cite St. Clair Springs Hotel Co. v. Balcomb, 215 Ala. 12, 108 So. 858 (1926), for the proposition that “a grantee of a widow holding a quarantine acquires no greater right as to [the heirs] against whom the adverse possession period of limitations does not run during life of a life tenant ([the widow]).” In St. Clair Springs, the property owner died, leaving a widow and four children, two of whom later died without issue. 215 Ala. at 13, 108 So. at 859. With regard to the claims to the subject property in that case by one of the children’s heirs, our supreme court observed that “[t]he possession of a widow under her quarantine right is not adverse and confers no greater or superior title to her grantee” and-that her grantee under a purported conveyance has no greater right as to the reversioners “who had no right of action for the recovery of possession during the life of the life tenant, and during such time limitations do not run against them for the recovery of possession.” 215 Ala. at 14, 108 So. at 860. As noted, however, unlike in St. Clair Springs, the widow in the present case did not remain in possession of the disputed property, she abandoned any dower rights to the disputed property, and she did not possess quarantine rights in the disputed property at any time. Because the circumstances of St. Clair Springs are distinguishable from the circumstances of the present case, we conclude that the rules of law expressed in Leddon remain applicable here.
The trial court quoted in its judgment the following excerpt from Marino v. Smith:
“Upon the death of a husband, a widow has a right of dower, which is not a *916property right but an equity; and it does not become a property interest until there has been an assignment thereof. Gillian v. Gillian, 340 So.2d 785 (Ala.1976); United States v. Hiles, 318 F.2d 56 (5th Cir.1963); Alabama Code (1975), § 43-8-114. Dower does not vest automatically in the widow but is allocated only on petition of the widow, heirs, or other interested parties. Gillian, 340 So.2d at 787. Liddie not only failed to have her husband’s estate probated, but she also failed to have her dower set aside.
“The widow is entitled to quarantine as an incidental right to dower. Hale v. Cox, 240 Ala. 622, 200 So. 772 (1941). The right of quarantine exists before dower is assigned and continues during the widow’s lifetime. Id. Failure to have dower assigned, and permitting the widow to retain possession without more, does not deprive the owner of the fee in the land. Lynch v. Jackson, 235 Ala. 90, 177 So. 347 (1937).
“It has been recognized that a widow retaining possession by virtue of her quarantine rights may acquire title by adverse possession. Taylor v. Russell, 369 So.2d 537 (Ala.1979); White v. Williams, 260 Ala. 182, 69 So.2d 847 (1954); Branford v. Shirley, 241 Ala. 314, 2 So.2d 403 (1941). However, a widow whose dower remains unassigned cannot acquire title by adverse possession as against heirs simply by remaining in possession of her husband’s land. Taylor, 369 So.2d at 541.
“In order for the widow to obtain title by adverse possession she must repudiate the title of her husband and disavow any claim to such title and give notice of the disavowal, and that notice must be brought home to the heirs. Id. If possession is open, notorious, and visible, a presumption of notice may arise. Id. at 542. However, it should be noted that all presumptions are favorable to the title, and possessions are not presumed to be hostile to it. White, 260 Ala. at 187, 69 So.2d at 851. To change a permissive or otherwise nonhostile possession into one that is hostile, there must be either actual notice of the hostile claim or acts or declarations of hostility so manifest and notorious that actual notice will be presumed. Id.”
454 So.2d at 1382 (footnote omitted).
The heirs argue that, in accordance with Marino, the widow’s possession of the disputed property could not deprive the heirs of their fee ownership of the disputed property, that the widow possessed the disputed property via the Board’s possession, and that the trial court erred in concluding otherwise. Again, the heirs fail to cite any authority indicating that the widow continued to be in possession of the disputed property following her purported conveyance of the property to the Board. In Wilder v. Mixon, 442 So.2d 922, 924 (Ala.1983), our supreme court observed that, until the date of the judicial assignment of dower, the widow “has no right ‘to enter and occupy any part of her deceased husband’s estate or to retain possession thereof as against the heirs or those claiming under them.’ ” (Quoting G. Thompson, Commentaries on the Modem Law of Real Property § 1919 (1979 Repl.).) The statutory right of quarantine does not apply to the disputed property, as discussed above. Thus, to the extent the Board “stepped into the shoes” of the widow, as argued by the heirs, the Board did not have any right to enter and occupy the disputed property despite the widow’s purported conveyance of the disputed property to the Board. Additionally, because, as we have determined, any remaining right held by the widow to claim her dower interest would have expired upon her purported conveyance of the property to the Board, the heirs could have brought an ejectment action against the Board as the result of its *917possession following that purported conveyance. See, e.g., Wallace v. Hall’s Heirs, 19 Ala. 367, 873 (1851).
The heirs next argue that the trial court erred in concluding that the Board’s possession of the disputed property was hostile and adverse to the heirs. They argue that the Board occupied and possessed the disputed property with the permission of the widow. The heirs cite no authority, however, in support of their assertion that the widow’s purported conveyance of 'the disputed property to the Board in fee simple resulted in the permissive occupancy by the Board that could not ripen into adverse possession. See Sea Calm Shipping Co., supra. Moreover, as discussed above, the widow’s purported conveyance would have amounted to an effective abandonment of the widow’s right to dower; thus, the widow cannot be said to have had any remaining rights to the disputed property such that she could allow its permissive use by the Board. “The burden of proving the possession adverse—that it was taken and held under a claim of title hostile to the title of the true owner—rests upon the party asserting it.” Dothard v. Denson, 72 Ala. 541, 545 (1882). In the present case, the widow was not the true owner of the disputed property at the time she purported to convey the property to the Board. In Smith v. Persons, 285 Ala. 48, 55, 228 So.2d 806, 811 (1968), our supreme court observed that, when the occupant of the land at issue in that ease went into possession with permission of a widow who was entitled to possession under her quarantine rights, the occupant’s possession would be regarded as continuing as permissive “unless disclaimed by declarations or acts unmistakably hostile, the equivalent of an abandonment or termination of the quarantine to which the widow was entitled, of which the heirs or cotenants had notice [or] knowledge, or which were so open and notorious that notice or knowledge must be imputed to them.” In the present case, in accordance with Smith, even if the widow had a right of dower in the disputed property, she abandoned that right upon her purported conveyance of the property to the Board, at which time any permission given by her to the Board to occupy the disputed property would have ripened into hostile possession against the heirs.
The heirs next argue that the trial court erred in entering a summary judgment in favor of the Board because, they say, a governmental entity cannot acquire title to real property by adverse possession without providing just compensation. The heirs fail, however, to cite any authority in support of that argument, see Sea Calm Shipping Co., supra, and state, instead, that they have found “[n]o Alabama case on point.” Moreover, we note that, in Morgan v. Alabama Power Co., 469 So.2d 100, 102-03 (Ala.1985), our supreme court determined that Alabama Power Company, an entity with the right of eminent domain, see Alabama Elec. Coop., Inc. v. Watson, 419 So.2d 1351 (Ala.1982), and Alabama Power Co. v. Taunton, 465 So.2d 1105, 1110 (Ala.1984) (Torbert, C.J., dissenting), had satisfied the common-law requirements of adverse possession such that it had acquired ownership of property previously belonging to a private citizen. Thus, the hems’ argument that the Board could not have acquired title to the disputed property by adverse possession is without merit.
We now turn to the heirs’ inverse-condemnation claim.
“A formal condemnation proceeding is a legal action brought by a condemning authority, such as the Government, in the exercise of its power of eminent domain. ‘Inverse condemnation’ refers to a legal action against a governmental authority to recover the value of property that has been taken by that govern*918mental authority without exercising its power of eminent domain—it is a shorthand description of the manner in which a landowner recovers just compensation for a taking of his property when the taking authority has not initiated condemnation proceedings. Condemnation proceedings require affirmative ‘taking1 action on the part of the condemning authority; the particular action required depends on the particular statute applicable. However, in inverse condemnation actions, a governmental authority need only occupy or injure the property in question; when that occurs and the property owner discovers the encroachment, the property owner has the burden of taking affirmative action to recover just compensation.”
Jefferson Cty. v. Southern Natural Gas Co., 621 So.2d 1282, 1287 (Ala.1993).
Based on its determination that the Board had adversely possessed the disputed property such that it had acquired ownership thereof, the trial court concluded that, for purposes of inverse condemnation, there had been no taking of the disputed property by the Board. The trial court cited Texaco, Inc. v. Short, 454 U.S. 516, 530, 102 S.Ct. 781, 70 L.Ed.2d 738 (1982), in which the United States Supreme Court observed that, after the abandonment of a mineral interest in property for a period of 20 years and “for which no statement of claim has been filed as abandoned,” the former owner retains no interest for which he or she may claim compensation and that, in such a case, there is “no ‘taking’ that requires compensation.” The trial court also cited a number of cases from other jurisdictions in support of its conclusion that there had been no taking, noting that the hems had failed to distinguish or disagree with any of the authority cited or to cite any authority in support of their position. Similarly, on appeal, the heirs fail to cite any authority indicating that, despite the Board’s adverse possession of the disputed property such that it had acquired ownership of the property, there had been a taking of the property for purposes of inverse condemnation. The hems cite Commonwealth v. Stephens, 407 S.W.2d 711 (Ky.1966), a case cited by the trial court as confirming the availability of ownership by adverse possession to a governmental entity in the Commonwealth of Kentucky, for the proposition that a private landowner whose land is claimed by the Commonwealth of Kentucky by adverse possession has “a remedy in the form of a reverse condemnation proceeding against the state.” 407 S.W.2d at 712-13. We note, however, that that statement was made to confirm that, before the governmental entity could acquire ownership by adverse possession, the private landowner has a remedy of “reverse condemnation” to stop the running of the statutory period for adverse possession. 407 S.W.2d at 712-13. In the present case, the heirs do not argue that they filed their inverse-condemnation claim before the statutory period for ownership by adverse possession had run with regard to the disputed property. Thus, any such argument is waived, see Gary v. Crouch, 923 So.2d 1130, 1136 (Ala.Civ.App.2005) (“arguments not raised by the parties [on appeal] are waived”), and Commonwealth v. Stephens does not support the heirs’ claim that the trial court erred in concluding that the Board had adversely possessed the disputed property in the present case.
The hems also argue on appeal that the trial court erred in concluding that the rule of .repose and the statute of limitations bar their inverse-condemnation claim. “[T]he rule of repose ‘bars actions that have not been commenced within 20 years from the time they could have been commenced.’ Tierce v. Ellis, 624 So.2d 553, 554 (Ala.1993) (emphasis added).” *919Willis v. Shadow Lawn Mem’l Park, 709 So.2d 1241, 1243 (Ala.Civ.App.1998). With regard to the rule of repose, the heirs argue that the Board’s taking of the disputed property by adverse possession would not be complete until the expiration of 10 or 20 years, depending on the type of adverse possession at issue, from the time the Board began possessing the disputed property in 1988, and, therefore, they argue, the rule of repose would not expire until 2018. We note, however, that 20 years from 1988 is 2008, not 2018. Because the heirs did not file their complaint until 2014, their argument that the rule of repose did not apply if it began to run in 1988 is without merit.
With regard to the statute of limitations, the heirs argue that their inverse-condemnation claim was filed as a counterclaim to the Board’s claim of ownership based on adverse possession. They argue that, based on Rule 13(c), Ala. R. Civ. P., which provides, in pertinent part, that “[a]ll counterclaims other than those maturing or acquired after a pleading shall relate back to the time the original plaintiffs claim arose,” their inverse-condemnation “counterclaim” relates back to the date the Board was entitled to claim the disputed property by adverse possession. The trial court concluded with regard to that argument, among other things, that the heirs’ inverse-condemnation claim cannot be construed as a counterclaim; that the heirs failed to cite any authority indicating that Rule 13(c) applies to property claims or equitable claims such as those at issue in the present case; that statutory adverse possession and adverse possession by prescription are not causes of action but rules of law that affirmatively establish title in the adverse possessor; that no cause of action was required to establish the Board’s ownership of the disputed property because it arose by operation of law; that adverse possession is not a separate cause of action; and that the heirs’ argument that their claim relates back to the date the Board could claim adverse possession of the disputed property would create absurd results. The heirs have failed to respond to any of those statements by the trial court in addressing their argument with regard to Rule 13(c). Because the heirs have failed to cite any authority on appeal indicating that Rule 13(c) applies to their claim or that their inverse-condemnation claim was properly classified as a counterclaim, we affirm the trial court’s judgment with regard to its conclusion that the statute of limitations bars the heirs’ inverse-condemnation claim. See Sea Calm Shipping Co., supra.
To the extent the heirs argue that federal law also prohibits a governmental entity from taking a private citizen’s property without providing just compensation, we note that the heirs have failed to cite any authority indicating that, because the Board acquired the disputed property pursuant to adverse possession, there had been a taking in accordance with federal law such that the heirs were entitled to compensation. Thus, that argument is waived, and the trial court’s judgment in favor of the Board on the heirs’ federal-law claim is affirmed. See Sea Calm Shipping Co., supra.
The heirs last argue on appeal that the trial court erred in entering a summary judgment in favor of the Board on the heirs’ unjust-enrichment claim.
“ ‘In order for a plaintiff to prevail on a claim of unjust enrichment, the plaintiff must show that
“ ‘ “the ‘ “defendant holds money which, in equity and good conscience, belongs to the plaintiff or holds money which was improperly paid to defendant because of mistake or fraud.” ’ Dickinson v. Cosmos Broad. Co., 782 So.2d 260, 266 (Ala.2000) (quoting Hancock-Ha*920zlett Gen. Constr. Co. v. Trane Co., 499 So.2d 1385, 1387 (Ala.1986)).... ‘The doctrine of unjust enrichment is an old equitable remedy permitting the court in equity and good conscience to disallow one to be unjustly enriched at the expense of another.’ Battles v. Atchison, 545 So.2d 814, 815 (Ala.Civ.App.1989).”
‘“Avis Rent A Car Sys., Inc. v. Heilman, 876 So.2d 1111, 1123 (Ala.2003). “ ‘One is unjustly enriched if his retention of a benefit would be unjust.’ ” Welch v. Montgomery Eye Physicians, P.C., 891 So.2d 837, 843 (Ala.2004) (quoting Jordan v. Mitchell, 705 So.2d 453, 458 (Ala.Civ.App.1997)). The retention of a benefit is unjust if
“ ‘ “ ‘(1) the donor of the benefit ... acted under a mistake of fact or in misreliance on a right or duty, or (2) the recipient of the benefit ... engaged in some unconscionable conduct, such as fraud, coercion, or abuse of a confidential relationship. In the absence of mistake or misre-liance by the donor or wrongful conduct by the recipient, the recipient may have been enriched, but he is not deemed to have been unjustly enriched.’ ”
“‘Welch, 891 So.2d at 843 (quoting Jordan, 705 So.2d at 458). The success or failure of an unjust-enrichment claim depends on the particular facts and circumstances of each case. Heilman, supra.’
“Mantiply v. Mantiply, 951 So.2d 638, 654-55 (Ala.2006) (emphasis omitted).”
Presley v. B.I.C. Constr., Inc., 64 So.3d 610, 625 (Ala.Civ.App.2009).
In Lewis v. Johnson, 507 So.2d 918, 919-21 (Ala.1987), our supreme court affirmed a judgment concluding that the plaintiffs in that case, whose deed to the property was invalid, had adversely possessed property for which the defendant had presented a deed claiming ownership. The defendant contended that he had an equitable lien on the property. Id. at 921. Our supreme court determined in Lems that the plaintiffs were “not guilty of wrongdoing or culpable conduct,” but that they had “merely been living on property that they thought they had a valid deed to,” and that they had “done nothing to bring about any hardship that [the defendant] may have to suffer.” Id. Similarly, in the present case, the Board was merely possessing property that it thought it had a valid deed to by virtue of the widow’s purported conveyance of the disputed property. Thus, we conclude, based on Lewis, that the heirs are not entitled to the equitable relief sought in their unjust-enrichment claim, and, therefore, we affirm the trial court’s judgment in favor of the Board on their unjust-enrichment claim.
Because the heirs have failed to raise any arguments on appeal that merit reversal of the trial court’s summary judgment, that judgment is affirmed.
AFFIRMED.
THOMPSON, P.J., and PITTMAN, THOMAS, and DONALDSON, JJ., concur.