Most courts give great deference to the parents of children in child custody matters, and grandparents are awarded custody of their grandchildren only under limited circumstances.

For example, if both parents are unfit to have custody of their children, or if both parents are deceased, or if one parent is deceased and the other is in prison, grandparents may petition the court for custody of their grandchildren.

And grandparent visitation rights vary from state to state, and are often conditioned on certain circumstances, such as when the child’s parents are divorced, separated, or deceased.

In Arizona, the law recognizes the primacy of parents' rights in child custody matters. However, under certain circumstances, grandparents can be awarded custody or visitation rights. According to Arizona Revised Statutes Section 25-409, grandparents may petition the court for visitation rights if the parents are divorced, one or both parents are deceased, or the child was born out of wedlock and the parents are not married. For custody, grandparents may seek legal decision-making authority or placement if it is deemed significantly detrimental for the child to remain or be placed in the custody of either parent. The court will consider the best interests of the child, taking into account factors such as the historical relationship between the child and the grandparent, the motivation of the parties involved, and the quantity of visitation time requested. The court gives special weight to the parent's opinion, but if the grandparent can demonstrate that the child's welfare is at significant risk, the court may grant custody to the grandparent. It's important to note that these matters are complex and outcomes can vary, so consulting with an attorney for specific cases is advisable.