What is the burden of persuasion for a motion to change custody based on a parent's relocation?

We conclude that the same allocation of the burden of persuasion applies in the case of a custodial parent's relocation as in any other proceeding to alter existing custody arrangements: "[I]n view of the child's interest in stable custodial and emotional ties, custody lawfully acquired and maintained for a significant period will have the effect of compelling the noncustodial parent to assume the burden of persuading the trier of fact that a change [in custody] is in the child's best interests." (Burchard v. Garay, supra, 42 Cal.3d at p. 536, 229 Cal.Rptr. 800, 724 P.2d 486.) ⁹

Similarly, the same standard of proof applies in a motion for change in custody based on the custodial parent's decision to relocate with the minor [13 Cal.4th 38] children as in any other matter involving changed circumstances: "[O]nce it has been established [under a judicial custody decision] that a particular custodial arrangement is in the best interests of the child, the court need not reexamine that question. Instead, it should preserve the established mode of custody unless some significant change in circumstances indicates that a different arrangement would be in the child's best interest." (Burchard v. Garay, supra, 42 Cal.3d at p. 535, 229 Cal.Rptr. 800, 724 P.2d 486.)