Elgin and Carol W., the maternal grandparents of Jeffrey A.W., appeal from orders dismissing their petitions for custody, guardianship and visitation. The parental rights of Jeffrey's biological father and mother were terminated in an earlier pro*39ceeding, and his guardian ad litem and the Dane County Department of Human Services, in whose custody Jeffrey had been placed pursuant to an earlier CHIPS (Child in Need of Protection and Services) adjudication, opposed the petitions, arguing that the termination of their daughter's parental rights to Jeffrey — and his adoption by another couple — precluded Elgin and Carol from establishing their claims as a matter of law. The trial court agreed and dismissed the petitions.
Elgin and Carol appeal, arguing that the trial court's dismissal orders were in error because: (1) they have a statutory right to petition for Jeffrey's custody and guardianship; (2) their petition for visitation stated an "equitable" claim pursuant to the supreme court's decision in Holtzman v. Knott, 193 Wis. 2d 649, 533 N.W.2d 419 (1995); and (3) the court's orders violate their constitutional rights in several respects. We reject their arguments and affirm the orders.
Jeffrey was born in 1988 and for the first three years of his life his parents changed their residence many times, occasionally living in Elgin and Carol's home. In December 1991, when his mother was imprisoned (his father had deserted them), Jeffrey and his older half-brother, Jeremy, were temporarily placed in Elgin and Carol's home. In April 1994, Elgin and Carol turned Jeffrey over to the department and he was placed in a foster home, where Elgin and Carol continued to visit him. In June 1996, Jeffrey's mother's and father's parental rights were terminated and, several weeks later, his foster parents petitioned to adopt him. Problems arose during the department's investigation of the petition, however, and Jeffrey was placed with a second set of foster parents, Jeff and Tamra T., on February 6,1997.
*40After Jeffrey's placement with Jeff and Tamra, Elgin and Carol began visiting him at Jeff and Tamra's home. A week or so later, however, after receiving reports of concern from Jeffrey's teachers, therapist and foster parents regarding his "emotional/behavioral ups and downs" following the visits, the department suspended Elgin's and Carol's visitation rights in order to permit Jeffrey to "get 'on an even keel' emotionally in his present foster home and at school."
On March 27,1997, Elgin and Carol filed petitions requesting custody of Jeffrey. They also petitioned for guardianship and adoption and for an order granting them visitation rights. The department moved to dismiss the adoption, guardianship and custody petitions, and denied that Elgin and Carol were entitled to visitation. With the parties' consent, the court referred the visitation issues to the Dane County Family Court Counseling Service to see whether some agreement on visitation could be reached. While the matter was still pending with the Counseling Service, Jeffrey continued to live with Jeff and Tamra, and in mid-August, after he had been with them for approximately six months, they petitioned to adopt him. The department conducted a home study and approved them as an adoptive family.
Elgin and Carol moved to intervene in the adoption proceedings, and the trial court consolidated all pending proceedings affecting Jeffrey for disposition. At the hearing on the department's motions, the department orally moved to dismiss the visitation petition in addition to the others. After a hearing, the trial court granted the department's motions to dismiss the adoption, guardianship and custody petitions, and denied Elgin and Carol's motion to intervene in Jeff and Tamra's adoption proceedings. It refused to dis*41miss the visitation petition, however, when Elgin and Carol's attorney submitted information from Jeffrey's therapist. A few weeks later, the court granted the motions for reconsideration of the department and Jeffrey's guardian ad litem and dismissed the visitation petition as well.
Shortly thereafter, on the eve of the hearing of Jeff and Tamra's adoption petition, Elgin and Carol asked the court to stay the proceedings pending their appeal of the dismissal orders. They did not appear at the adoption hearing the following day and the court dismissed their motion for a stay as untimely. The hearing proceeded and the court approved Jeffrey's adoption by Jeff and Tamra, endorsing their stated willingness to allow Jeffrey to visit with Elgin and Carol as long as Elgin and Carol would accept the fact that Jeffrey was now a member of their (Jeff and Tamra's) family.
I. The Guardianship and Custody Petitions1
The department maintains that these issues are moot because of Jeffrey's subsequent adoption by Jeff and Tamra. We agree. An issue is moot "when a determination is sought which, when made, cannot have any practical effect upon an existing controversy." City of Racine v. J-T Enters. of Am., Inc., 64 Wis. 2d 691, 700, 221 N.W.2d 869, 874 (1974) (internal quotation marks and quoted source omitted). As a general matter, "if a question becomes moot through a change in circumstances, it will not be determined by the reviewing court." Id. at 701, 221 N.W.2d at 875 (internal quota*42tion marks and quoted source omitted); see also Riley v. Lawson, 210 Wis. 2d 478, 490, 565 N.W.2d 266, 271 (Ct. App. 1997).
After an adoption, "the relation of parent and child and all the rights, duties and other legal consequences of the natural relation of child and parent thereafter exists between the adopted person and the adoptive parents." Section 48.92(1), STATS. Because Jeff and Tamra are now Jeffrey's parents, a person seeking transfer of his custody or guardianship must demonstrate that Jeff and Tamra are unfit parents. See Barstad v. Frazier, 118 Wis. 2d 549, 568, 348 N.W.2d 479, 489 (1984) (parents are entitled to custody of their children unless found to be unfit or unable to care for them, or for other "compelling reasons"). In this case, the trial court, reviewing Jeff and Tamra's adoption petition, found that they were not only fit and suitable but "perfect for this child in every way."
It is apparent, therefore, that Jeff and Tamra's adoption of Jeffrey determined any and all issues relating to Elgin's and Carol's custody and guardianship petitions, and in that sense these issues are indeed moot. Elgin and Carol argue, however, that even if we so rule, we should still consider their petitions because they raise "issues of great public importance" in an age when "[m]ore grandparents are helping raise their grandchildren." The supreme court has recognized that there are exceptions to the mootness rule.
This court has carved out certain exceptions to this general rule [of mootness] where: the issues are of great public importance; the constitutionality of a statute is involved; the precise situation under con*43sideration arises so frequently that a definitive decision is essential to guide the trial courts; the issue is likely to arise again and should be resolved by the court to avoid uncertainty; or, a question is capable and likely of repetition and yet evades review because the appellate process usually cannot be completed and frequently cannot even be undertaken within a time that would result in a practical effect upon the parties.
Jones v. Gerhardstein, 141 Wis. 2d 710, 723-24, 416 N.W.2d 883, 888 (1987) (quoted source omitted).
Elgin and Carol argue that this case fits most, if not all, of those exceptions because "the lines between grandparents and parents [are] becoming] blurred," causing more grandparents to "seek[ ] rights to see and raise their grandchildren." Beyond that, the argument is unamplified and unexplained, and we find it unpersuasive.
There is more here than usually is found in a moot case — where relief is barred because of a change in the parties' positions or relationships. With Jeffrey's adoption, there has been a basic and significant change in the parties' legal status under authority that is both long-standing and plain in its import. To grant Elgin and Carol the relief sought in their petitions would necessitate ignoring the legal effect of the termination of his parents' parental rights and undoing the completed adoption — which, as we have noted, has not been challenged on appeal. Even if we had the authority to do so — which we neither assume nor decide — they have not persuaded us that we should make such an attempt.
*44II. The Visitation Petition
Elgin and Carol base their claim for visitation on Holtzman, where the supreme court held that, under certain circumstances, visitation may be ordered in situations not contemplated or authorized by statute, upon "equitable" considerations, when it is determined to be in the child's best interest. They claim their petition alleges facts which, under Holtzman, entitle them to trial.
In Holtzman, two women, S.H. and H.K., who had maintained a relationship for many years, decided to raise a child together and H.K. was artificially inseminated. When the child was five years old, H.K. left the relationship, taking the child with her. S.H. brought an action seeking custody and visitation. The trial court dismissed the action, concluding that (1) the statutes require a finding of parental unfitness before custody may be awarded to a non-parent, and there was no triable issue with respect to H.K's fitness, and (2) the visitation request was groundless because the applicable statute, § 767.245, Stats., applies only to "actions affecting the family," and with dismissal of the custody petition, no such action was pending.
The supreme court reversed the trial court's dismissal of S.H.'s visitation petition. It began by noting that, unlike other aspects of divorce and parent-child relationships — notably custody and adoption — courts derive their authority to order visitation not from the statutes but from the common law. Holtzman, 193 Wis. 2d at 681-82, 533 N.W.2d at 430. The court then examined all the statutes dealing with visitation and concluded that nothing in their terms suggested that the legislature had intended to bar the courts from exercising their common-law equitable powers "to *45order visitation in circumstances not included within the statutes but in conformity with the policy directions set forth in the statutes." Id. at 682-83, 533 N.W.2d at 431. The court concluded by setting out a two-part test for determining when it would be appropriate for trial courts to exercise such equitable powers:
[W]e conclude that a circuit court has equitable power to hear a petition for visitation when it determines that the petitioner has a parent-like relationship with the child and that a significant triggering event justifies state intervention in the child's relationship with a biological or adoptive parent. . . . Only after the petitioner satisfies this burden may a circuit court consider whether visitation is in the best interest of the child.
Id. at 694, 533 N.W.2d at 435.2 The court remanded the case to the circuit court to apply the test. Id. at 695-96, 533 N.W.2d at 436.
Elgin and Carol maintain that they are in the same position as the petitioner in Holtzman. The department and Jeffrey's guardian ad litem disagree; *46they argue that Holtzman is distinguishable on the facts, on the law, and in light of the underlying policy considerations of the children's code; and they contend that it does not give Elgin and Carol the rights they claim. Again, we agree.
While the parties in Holtzman were denied access to a legally recognized marriage, the situation was in many ways indistinguishable from that existing in a "traditional" divorce proceeding: resolving custody and visitation issues in the context of the breakup of a longstanding, intact family. The petitioner was the equivalent of the child's parent, planning its birth and living with the child and its biological mother in a parental/spousal relationship until she and the child's mother separated.
We face a significantly different situation here, not only on the facts but also in the interplay of other statutes designed to promote and protect Jeffrey's best interests. Jeffrey's custody was transferred from his biological parents to the department after he had been adjudged a child in need of protection and services following his father's desertion and his mother's imprisonment; and that determination formed the basis of the subsequent termination proceedings. The termination order recited, among other things, that it was "likely that Jeffrey will be adopted after termination,"3 and, after dissolving all parental "rights, powers, privileges . . . duties and obligations . . . existing between the parent and child," it placed Jeffrey in the custody of the department "pending adoptive placement." Although it is not part of the record, we assume from the language of the court's *47order that the permanency plan the department is required to prepare for Jeffrey in such circumstances, see § 48.38, STATS., contemplated his adoption.
We appreciate the continued existence of the common-law equitable authority of the courts to order visitation in extra-statutory situations. But we agree with the department and Jeffrey's guardian ad litem that those rights, as delineated in Holtzman, should not trump the comprehensive, best-interest-of-the-child provisions of ch. 48, Stats. — particularly those dealing with termination of parental rights and adoption. The supreme court has said, for example, that the child's best interest is the "polestar of all determinations under ch. 48," Brandon S.S. v. Laura S., 179 Wis. 2d 114,149, 507 N.W.2d 94, 107 (1993), and represents "unequivocally . . . the overall and underlying legislative policy" in all TPR proceedings. M.W. and I.W. v. Monroe County Dep't of Human Servs., 116 Wis. 2d 432, 442, 342 N.W.2d 410, 415 (1984).
The net result of the prior proceedings involving Jeffrey and his family — both "old" and "new" — has been a full and final determination that it is in his best interest that his biological parents' rights be terminated and that he be adopted by Jeff and Tamra. The termination proceedings completely and irrevocably severed all their parental bonds and relations with Jeffrey, and the supreme court has recognized that termination of parental rights has the same effect on the relationship between members of the parents' families and the child as it has on the parent-child relationship. See Brandon S.S., 179 Wis. 2d at 147, 507 N.W.2d at 106 (termination of parental rights "transforms the legal relationship not only between parent *48and child, but also between the parent's family and the child").
Another important aspect of any TPR proceeding — and any adoption proceeding — is the finality of the result. Indeed, the supreme court has said that finality of the circuit court's decision is "critical" in such cases. T.M.F. v. Children's Serv. Soc'y of Wisconsin, 112 Wis. 2d 180, 187, 332 N.W.2d 293, 297 (1983). The reasons are obvious: the longer the child remains in limbo, the longer it takes for him or her to shake the dislocation and trauma associated with an uncertain family situation. And we agree with the department and Jeffrey's guardian ad litem that applying Holtz-man to the distinct facts of this case would be inimical to that end, as well as to the underlying purposes of the earlier termination and adoption proceedings, for it would permit relatives of the biological parents — or anyone else filing a petition alleging the Holtzman basics — to survive a motion to dismiss and proceed to a trial that would throw the child and his adoptive parents right back into the very type of unsettling, traumatic atmosphere that should have come to closure long ago.
This case is a prime example of the need for finality. Jeffrey's association with his biological parents was spotty and intermittent almost from the date of his birth. In 1991, when he was three years old and essentially had been abandoned by his parents, he was taken into the department's custody. He lived for a time with Elgin and Carol and then with two sets of foster parents. His parents' parental rights were terminated in 1996, and his adoption by Jeff and Tamra was not finalized until November 1997. It is true, as they stress in their brief, that Elgin and Carol have pled the basic *49"equitable" components of the Holtzman holding in their petition. As the department points out, however, we have recognized that" 'equity' [does not] mean that a court may ignore statutes and case law to enable it to assist someone in trouble. A court's equitable powers are not that all-encompassing." First Federated Sav. Bank v. McDonah, 143 Wis. 2d 429, 434, 422 N.W.2d 113, 115 (Ct. App. 1988). To adopt Elgin and Carol's position that every proceeding, every investigation, and every adjudication that has taken place to this point can and should be undone to permit trial of their Holtzman-hased equitable claim would, in our opinion, run contrary not only to the termination-of-parental-rights and adoption laws themselves but to the important public policy considerations underlying them — especially the "polestar" best-interest-of-the-child policy. None of these considerations were implicated in Holtzman and, for all these reasons, we decline to extend the court's holding in that case to the situation presented on this appeal.4
*50III. Constitutional Arguments
Elgin and Carol also raise several constitutional challenges to the trial court's orders. They argue first that their due process rights were denied because the court failed to follow "the rules of civil procedure and the basic tenets which follow them" in dismissing their petitions. They don't explain the argument further, other than to state that, had the court followed accepted procedural rules and "tested the legal sufficiency" of their petitions — in other words, if the court had not dismissed their petition — they "would have prevailed under [Holtzman] and the plain meaning of the statutes." We reject the argument. First, Elgin and Carol fail to explain how an alleged error in following state procedural rules can give rise to federal or state constitutional claims. Second, as we held earlier in this opinion, Holtzman is inapplicable.
Elgin and Carol next claim that the trial court's consideration of an affidavit containing information from Jeffrey's therapist, which his guardian ad litem filed as an attachment to her motion seeking reconsideration of the court's initial decision not to dismiss the visitation petition, violated their due process and con*51frontation rights.5 As we noted above, the trial court, after dismissing Elgin and Carol's adoption, custody and guardianship petitions, decided not to dismiss the visitation petition on the basis of information in a letter from Jeffrey's therapist which their attorney gave to the court. Jeffrey's guardian ad litem accompanied her motion for reconsideration with an affidavit containing information from the therapist that corrected (and disputed) much of the information Elgin and Carol's attorney had provided at the earlier hearing. The guardian offered the affidavit to support her argument that the therapist's comments submitted by Elgin and Carol were taken out of context, and that the court should not consider any extraneous information on the motion to dismiss the visitation petition, but rather should decide as a matter of law that their visitation petition fails to state a claim. The court granted the guardian ad litem's motion, stating in its decision that the guardian was "correct in [her] assertions and arguments in this regard." The court went on to specifically "adopt the rationale set forth in the [guardian's] brief . . . as [the court's] own rationale." In these circumstances, we see no violation of Elgin's or Carol's rights to due process or confrontation. In other words, the court decided to dismiss the visitation petition as a matter of law, and Elgin and Carol have not persuaded us that that decision was constitutionally defective.
*52They next argue that the court's orders violated their rights to equal protection and due process of law. They state generally that they have a "liberty interest" in maintaining a relationship with Jeffrey, and they claim the trial court violated that interest when it dismissed their visitation petition. They offer no authority for the proposition, however, other than to cite (without discussion or page references) several United States Supreme Court cases that appear to us to be beside the point. Here, too, they have not persuaded us that the trial court's decision violated their rights to equal protection and due process of law.
By the Court. — Orders affirmed.
Elgin and Carol have not appealed from the trial court's dismissal of their own adoption petition and their motion to intervene in Jeff and Tamra's adoption proceedings.
According to Holtzman, in order to establish the existence of a parent-like relationship with the child, the petitioner must prove four elements: (1) that the biological or adoptive parent consented to, and fostered, his or her formation and establishment of such a relationship with the child; (2) that the petitioner and child lived together in the same household; (3) that the petitioner assumed obligations of parenthood "by taking significant responsibility for the child's care, education and development, including contributing towards the child's support, without expectation of financial compensation"; and (4) that the petitioner "has been in a parental role for a length of time sufficient to have established with the child a bonded, dependent relationship parental in nature." Holtzman v. Knott, 193 Wis. 2d 649, 694-95, 533 N.W.2d 419,435-36 (1995).
At that time, as discussed above, Jeffrey's then-foster parents were planning to adopt him, but they eventually withdrew their petition.
Elgin and Carol also argue that the department should be "equitably estopped" from seeking dismissal of their visitation petition because the department agreed to try to reach a negotiated settlement of the visitation issue — by having it referred to the Dane County Family Court Counseling Service — prior to trial, and because, during that time, Jeff and Tamra applied to adopt Jeffrey. They do not explain the argument further, other than to assert that, as a result of the FCCS referral, they felt "no sense of urgency" to have their petition heard in court and that, had they not "relied on the Department's actions" in this regard, their petition would have moved ahead faster.
The department responds that, under well-settled law, the rule of equitable estoppel exists "to prevent the assertion of what would otherwise be an unequivocal right," and that "[s]uch an estoppel operates always as a shield, never as a sword. . . . and it does not of itself create new rights." Sporleder v. Hermes, *50162 Wis. 2d 1002, 1026, 471 N.W.2d 202, 212 (1991), overruled on other grounds by Holtzman, 193 Wis. 2d at 690, 533 N.W.2d at 434. Elgin and Carol have not replied to this argument, and we have held that the long-standing rule that a proposition advanced by an appellant is taken as confessed when the respondents do not undertake to refute it applies with equal force when the appellant fails in its reply brief to dispute arguments asserted by the respondent. Schlieper v. DNR, 188 Wis. 2d 318, 322, 525 N.W.2d 99, 101 (Ct. App. 1994). Elgin and Carol have not persuaded us that their equitable estoppel argument has any basis in law.
Here, and at various other points in their brief, Elgin and Carol attempt to assert and argue Jeffrey's rights as well as their own. Jeffrey is, of course, represented in these proceedings by his guardian ad litem, and Elgin and Carol have not provided us with any authority to support the proposition that they may assert violations of his constitutional rights in addition to their own.