*151This is a probate case concerning the distribution of approximately 538,556 square meters of land located in Rota known as “Inayan.” At issue is whether Inayan should be distributed to all eight children of Antonio Gogue Barcinas, the decedent, or, as the trial court held, to only five of them.
All of Antonio’s children have died except the estate administrator, Alejandro. (His son Juan died during the pendency of this action.) This appeal follows the judgment after remand from our earlier decision, In re Estate of Barcinas, 2 N.M.I. 437 (1992) (holding that hearsay within hearsay is admissible to show a decedent’s intent regarding advancements made to his children).
I.FACTS
Antonio Gogue Barcinas died intestate in 1952. He had eight children. While he was alive, Antonio transferred several hectares of land to three of his children: Maria, Juan and Jose.1
In 1963, the Trust Territory Land Title Office issued Title Determination 501, certifying that the “heirs of Antonio Gogue Barcinas,” represented by Antonio Blanco Barcinas as land trustee, owned the Inayan property. Barcinas, 2 N.M.I. at 439. On August 11, 1989, the NMI Land Commission issued a certificate of title to the same effect: that the land belonged to Antonio’s heirs.
On August 24, 1989, a petition for letters of administration was filed. On October 27, 1989, the administrator proposed to the trial court that Inayan, the only remaining estate asset, be distributed to all of Antonio’s children except Maria, Juan and Jose. The three objected and a hearing was held to determine whether advancements had been made to Maria, Juan and Jose, precluding them from taking a proportional share of the Inayan property. The only evidence of Antonio’s intent to preclude Maria, Juan and Jose from sharing in Inayan was hearsay testimony. The trial court rejected the testimony on the ground of hearsay. The estate’s administrator appealed that ruling.
We reversed the ruling excluding the hearsay testimony and remanded the case for a “new hearing consistent” with our opinion. Barcinas, 2 N.M.I. at 449. On remand, the hearsay testimony was admitted and the court awarded Inayan to Alejandro and the heirs of the other four children who did not receive any advancement. It excluded Maria, Juan and Jose from receiving a share in the Inayan land. The three have appealed.
II. ISSUES AND STANDARD OF REVIEW
1. Whether the trial court erred in failing to hold a new trial on remand.
2. Whether the nature of this action changed on remand from an intestacy action to the probate of an oral will.
3. Whether the trial court erred in distributing Inayan to only five of Antonio’s children.
4. Whether the trial court erred “in not accepting the unappealed determination of the Land Commission as to the ownership of the Inayan property.”
We review the first issue for abuse of discretion. Ito v. Macro Energy, Inc., 4 N.M.I. 46 (1993).
The second and fourth issues allege errors of law. Therefore our review is de novo. Rosario v. Quan, 3 N.M.I. 269 (1992). The third issue presents a mixed question of law and fact which we will review de novo. Id.
in. DISCUSSION
A. The Scope of Hearing on Remand
The appellants argue that our earlier mandate required the trial court to conduct a full rehearing that is a “full repeat of the last trial,” not the limited hearing they received. Trial Transcript at 3:11-14, In re Estate of Barcinas, Civ. No. 89-0850 (N.M.I. Super. Ct. Nov. 19, 1992). A full re-hearing was not what we required.
This Court remanded for a “new hearing consistent” with our opinion. Barcinas, 2 N.M.I. at 449. The trial court had the discretion, which it properly exercised, to allow the parties to introduce and rebut the hearsay testimony earlier excluded. A repeat of the various testimonies given at the first hearing would have been redundant. No offer of proof was made as to any evidence which the appellants were precluded from introducing. The appellants do not show us that they were prejudiced as a result of the limited hearing that was given. There being no abuse of discretion committed, we hold that the hearing held on remand was adequate.
B. The Nature of the Action on Remand
The only dispute in this matter involves the narrow issue of whether Antonio gave Maria, Juan and Jose advancements on their prospective inheritances. The initial hearing focused on that issue. The first appeal dealt with the issue of the admissibility of hearsay *152testimony bearing on the question of advancements. The scope of the hearing on remand was limited to determining whether there were advancements made to each of the appellants in light of the hearsay testimony that their father intended to exclude them from sharing in Inayan.
The appellants now assert that the nature of the action somehow changed on remand from an intestacy proceeding to the “probate of an oral will.” They argue that the trial court looked upon this matter as a proceeding to probate an oral will because it effectuated the “wishes and intent of the decedent” to distribute Inayan to the five children other than the appellants. As such, the court disregarded the fact that this was an intestacy matter, which (by definition, the appellants assert) means that the decedent died “without leaving anything to testify what his wishes were with respect to the disposal of his property after his death.” Juan and Jose’s Opening Brief at 13, citing Black’s Law Dictionary.2 As we understand their argument, the appellants contend that the decedent’s hearsay testimony was, in effect, an “oral will” which the trial court allegedly probated.
We disagree. It is not an “oral will” but merely a statement that because of the advancements the three received, they were not to share in the remainder of Antonio’s estate.
We are not persuaded that the nature of this matter changed, as the appellants suggest. It remains a dispute over whether Maria, Juan and Jose received advancements on their inheritances.
C. The Advancements Issue
The appellants’ main contention on appeal, though not clearly articulated in their briefs, is that the trial court failed to recognize and analyze the issue of advancements.
Because Antonio died before 1984, our probate code does not apply to the probate of his estate. See 8 CMC § 2102. Title 13 of the Trust Territory Code, which applies, has no provision on intestate succession. In re Estate of Cabrera, 2 N.M.I. 195, 203-204 (1991). We therefore must determine whether Chamorro custom applies in this case. Id. at 205.
Before he died, Antonio gave certain parcels of land to three of his children, the appellants. To the other five, he gave at most a sitio (village lot). The administrator, Alejandro, contends that Antonio intended to exclude the appellants from sharing in Inayan because Antonio had already given them other land. He argues that the transfers made to the appellants were “advancements.”
The trial court held that the decedent intended “that Inayan shall be distributed to the five children” who had not received agricultural lands. Conclusions of Law ¶ 3, Barcinas, supra (Dec. 18, 1992) (Findings of FactQ and Conclusions of Law). The trial court did not specifically state whether the transfers made to Maria, Juan and Jose were advancements. Instead it relied on a footnote (“footnote 8") in our first opinion in this case to apply the customary law, which formed the basis of its decision to distribute Inayan to the five children other than the appellants. The footnote states that the “wishes and intent of the decedent form the basis of [] intestate succession under Chamorro custom . . . and should be followed.” Id., Conclusion of Law ¶ 1; Barcinas, 2 N.M.I. at 444 n.8. The trial court therefore applied this “customary law” in this intestacy proceeding.
We agree with the appellants that a person who dies intestate leaves nothing “to testily to what his wishes were with respect to the disposal of his property after his death.” Juan and Jose’s Opening Brief at 13, citing Black’s Law Dictionary.3 “The ordinary meaning of intestacy is dying without having made a will disposing of property of the decedent.” In re Baird’s Estate, 287 P.2d 365, 372 (Cal. Ct. App. 1955).
The parties have asserted that Antonio died intestate. By necessary implication, this means that no form of customary testamentary distribution applies. The forms of customaiy distribution that we have recognized are partidas and testamentos.4 Each is based on the wishes and intent of the decedent. See In re Estate of Deleon Castro, 4 N.M.I. 102, 110 (1994). They are testamentaiy in nature because, like wills (a common law concept), the intent of the decedent, to the extent that it is established, controls the distribution of the decedent’s property.
Here, the administrator did not assert that Inayan should be distributed to the five children pursuant to a written or oral will, partida or testamento. He stated that *153his late father died intestate, and that Inayan should be distributed to the five because the three appellants received land from their father during their father’s lifetime. Because Antonio died intestate, it necessarily follows that there was no testament, legal or customary, directing how his estate should be distributed.
In other words, by claiming that Antonio died intestate, the administrator in a sense conceded that the wishes and intent of the decedent as to how his property should be distributed on his death were not clear. The administrator invoked a common law doctrine of intestate succession, that of advancements, as precluding the three appellants, who had already received a share of their father’s land holdings, from taking an equal share of Inayan, the remaining asset of Antonio’s estate. We emphasize that the administrator did not assert that the land should be distributed to the five children because of a will or the custom of partida or testamento.
The trial court’s application of the principle that the wishes and intent of the decedent should be followed would be proper in a customary distribution case (partida or testamento). However, in this intestate case where the wishes and intent of the decedent are, as a matter of law, unknown, it was not appropriate to apply such a principle. We therefore hold that the trial court erred in applying such standard as if it were a custom.5
Neither the parties nor the trial court set forth any Chamorro custom akin to the common law concept of advancements that resolves whether or not advancements were received by the three. We are not aware of any such custom because the doctrine of advancements is not known in Chamorro tradition. The concept of advancements is unique to the common law. Since there is no applicable customary law, we shall apply the common law. 7 CMC § 3401.
In the first appeal, we held that Antonio’s hearsay statement was admissible. In substance, the hearsay was that the five children should receive Inayan because the three appellants had previously received agricultural lands. This statement is relevant only to the disputed issue in this case: whether or not Antonio intended to transfer properties to the three appellants as gifts or as part of their prospective inheritances, i.e., as advancements.
The statement is irrelevant as to how Inayan, the remaining asset of the estate, may have been intended to be distributed by Antonio, because this is an intestate succession case in which the administrator’s clear and consistent position has been that Antonio died without making a customary or common law will (written or oral), partida, or testamento, in regard to how Inayan should pass. We are thus confined by the nature of this case, as was the trial court, to determine only whether advancements were made.
The common law doctrine of advancements is still viable today, though it has been codified in many jurisdictions. See National Conference of Commissioners on Uniform State Laws, Uniform Probate Code § 2-109, reprinted in 8 Uniform Laws Annotated (West 1983 & Supp. 1990)); Cal. Prob. Code § 6409 (1990). “An advancement is a perfect and irrevocable gift made by a parent during his lifetime to his child with the intention on the part of the donor that such gift shall represent a part, or the whole, of the portion of the donor’s estate that the donee would be entitled to on the death of the donor intestate.” In re Estate of Lee, 462 P.2d 492, 494 (Colo. 1969); see also In re Estate of Button, 830 P.2d 1216, 1219 (Kan. Ct. App. 1992); In re Estate of Martinez, 633 P.2d 727, 731 (N.M. Ct. App. 1981). The common law focuses on the decedent’s intent to determine whether an advancement was made.
The advancements doctrine is based on the assumption that a parent intends to treat all of his or her children equally. Clement v. Blythe, 248 S.W.2d 883, 885 (Ark. 1952); Lee, 462 P.2d at 494; Page v. Elwell, 253 P. 1059, 1062 (Colo. 1927). Therefore, when a child receives a substantial gift of real or personal property which was not intended for the purpose of maintaining that child, the common law imposes a presumption that an advancement was intended. Lee, 462 P.2d at 494; see also Clement, 248 S.W.2d at 885; Martinez, 633 P.2d at 731.
The presumption of an advancement is, however, rebuttable. The strength of evidence needed to rebut the presumption differs among the various jurisdictions. Martinez notes that the “clear and unmistakable,” “preponderance of the evidence” and “slight evidence” standards have been employed in advancement cases. Id., citing Annotation, Presumption and Burden of Proof with Respect to Advancements to Children, 26 A.L.R. 1106 (1923), amended by 31 A.L.R.2d 1036 (1953). *154Clement applied the preponderance of the evidence standard and noted that the “presumption is not especially a strong one.” 248 S.W.2d at 885. And, it may be “readily overcome by proof of actual intent.” Id. The court reasoned that there “may evidently be many reasons for a parent to think that one of his children should receive more than an exact share of the estate.” Id. We find the reasoning in Clement persuasive and hold that the presumption of an advancement may be rebutted by proof, established by a preponderance of the evidence, that property was intended to be a gift rather than an advancement.
Maria, Juan and Jose each received at least six hectares of land from their father during his lifetime.6 These transfers were substantial enough to invoke the presumption that advancements were intended by their late father. The hearsay testimony of Alejandro, the administrator and only living child of Antonio, supports the presumption that advancements were given the three, as does the testimony of the decedent’s daughter-in-law, Florida, whose testimony corroborated Alejandro’s testimony. The testimony of these two individuals establishes that because Antonio gave the appellants agricultural land prior to his death, they should be precluded from sharing in Inayan. The appellants already received a share of their father’s estate.
To rebut the presumption that advancements were given, the appellants presented the hearsay testimony of the appellant Jose, a grandson, that Antonio intended all of his children to share equally in Inayan. Having heard these testimonies, the trial court chose to believe the testimony of Antonio’s son and daughter-in-law, Alejandro and Florida, rather than his grandchild, Jose. This finding is not clearly erroneous, and shall stand.
The preponderance of the evidence standard is described as “evidence which is of greater weight or more convincing than the evidence which is offered in opposition to it; that is, evidence, which as a whole shows that the fact sought to be proved is more probable than not.” Black’s Law Dictionary 1182 (6th ed. 1990). In view of the relatively large parcels Antonio gave to Maria, Juan, and Jose, and the testimony of Alejandro and Florida, found credible by the trial court, the record establishes that the appellants failed to rebut the presumption that there was an advancement made to each of them. Based on the trial court’s decision and the record below, we hold that Maria, Juan and Jose each received advancements from their late father.
Our analysis does not end here, however. The advancements made to Maria, Juan and Jose do not altogether preclude them from sharing in some portion of Inayan so long as they bring the value of their advancements into “hotchpot.” The “hotchpot” doctrine refers to “the bringing into the estate of an intestate an estimate of the value of advancements made by the intestate to his or her children, in order that the whole may be divided in accordance with the statute of descents.” Page, 253 P. at 1061-62. At common law, an heir who received an advancement could elect to share equally in the value of the estate if he or she wished to bring his or her advancement into hotchpot. 3 Am. Jur. 2d Advancements [hereinafter Advancements] § 56 (1986); 26A C.J.S. Descent & Distribution § 106 (1956).
In hotchpot, if the value of an heir’s advancement is less than the value of his or her share in the estate, then that heir is entitled to the difference in the respective values. Advancements, supra, § 58, citing Simon v. Simon’s Estate, 122 N.W. 544 (Mich. 1909). If the advancement is greater than his or her respective share in the estate, then that heir will receive nothing from the estate, but will not lose the property which constitutes the advancement (because an advancement by definition is an irrevocable gift). Id.-, see also Cal. Prob. Code § 6409(a) (1990).
In order to receive a share in Inayan, the appellants must elect to bring the value of their advancements into hotchpot. Because we hold that advancements were given to Maria, Juan and Jose, we shall remand the case so that the appellants may be given the opportunity to elect to bring the value of their advancements into hotchpot. If the value of any individual appellants’ advancement is less than the value of his or her respective share in the estate, then he or she shall be entitled to the difference.
D. The Finality of the Land Commission Certificate of Title
The appellants’ last contention is that the Land Commission certificate of title is final and binding and the trial court did not have the discretion to change the meaning of the term “heirs of Antonio Gogue Barcinas.” They argue that because no appeal was taken from the Land Commission determination of ownership (upon *155which the 1989 certificate of title was based), the appellees can not seek to modify it now. See 2 CMC §§ 4249, 4251. They contend that the Superior Court had no jurisdiction to set aside the ownership determination. They further contend that the administrator presented no evidence as to why the certificate of title was not binding. Because the administrator failed to meet his burden showing that these determinations should be overturned, they argue that we should reverse the ruling below. We are not persuaded that we should do so.
This case involves the question of advancements made to certain heirs of Antonio. There is no dispute that Inayan is an asset of Antonio’s estate. When Antonio died, the land passed to all of his children, each of whom had a right to an equal share of the land. The determinative question here, however, is whether the transfers made to Maria, Juan and Jose were advancements, precluding them from sharing in Inayan with the other five children.
The sole issue before the trial court was how Inayan, the only remaining asset of Antonio’s estate, should be distributed in light of the advancements made to Maria, Juan and Jose. The Land Commission ownership determination does not bear on this question.
IV, CONCLUSION
The trial court’s decree is VACATED and this matter is REMANDED for further proceedings.
The trial court is directed to issue an order finding that advancements were received by Maria, Juan and Jose. It shall then give each appellant the opportunity to bring his or her advancement into hotchpot. If an election is made, the trial court shall then determine the amount of the advancement based on the record previously made by the parties. The trial court may order further hearings and briefings to determine the value of each advancement. Thereafter, the trial court shall distribute the estate accordingly.
We refer to Maria, Juan and Jose, each deceased, as “appellants” herein even though it is their respective heirs who maintain this action.
The appellants’ citation is to the fourth edition of Black’s Law Dictionary. This definition also appears in the sixth edition. See Black’s Law Dictionary 821 (6th ed. 1990).
See id.
A partida “occurs when the father calls the entire family together and outlines the division of the property among his children.” In re Estate of Deleon Castro, 4 N.M.I. 102, 110 (1994). A testamento is a “written partida, which preserves in writing the intent and directions of the male head of the family in regardQ to distribution of the family’s properly.” Id. We have also recognized the existence of traditional oral wills. In re Estate of Barcinas, 2 N.M.I. 437, 445 n.9 (1992), but we have yet to decide a case in which a traditional oral will is at issue.
Confusion has perhaps arisen because footnote 8 in our opinion in the first appeal states that the “wishes and intent” of the decedent should be followed in “intestate succession” cases. Id., 2 N.M.I. at 444 n.8. However, first, this dictum concerned the issue then on appeal, which was the admissibility of evidence, not the law of advancements. We held that hearsay evidence is admissible to show whether the decedent’s inter vivos transfers of land to his children were intended to be advancements on their respective inheritances, or gifts. Second, footnote 8 cited In re Estate of Cabrera, 2 N.M.I. 195 (1991), a partida case. We clarify footnote 8 by expressly stating that the wishes and intent of a decedent control in cases involving custom, such as partida or testamento, not in intestacy cases such as the one at hand.
Alejandro’s trial testimony revealed that Maria received approximately six hectares of land in “Apalalogo,” Rota, see Transcript at 10:16-19, In re Estate of Barcinas, Civ. No. 89-0850 (N.M.I. Super. Ct. Apr. 16, 1990), 6.9 hectares of land in “Chamuge,” Rota, id. at 10:12-15, and 1.4 hectares of land in “Nanmog,” Rota, id. at 11:1. Augusto Atalig testified that Maria received Chamuge and Nanmog for her services rendered to her parents and because she paid for her parents’ funeral expenses. Id. at 134:1-135:6. Alejandro testified that Maria received more land than the other two appellants because she took care of her parents. Id. at 42:4-6.