The answer to this depends on who has conservatorship. In Texas, child “custody” does not refer to which parent has the child living in their home. In fact, child “custody” refers to conservatorship, which is the rights and duties of the parents (i.e. to make decisions regarding educational decisions, medical decisions, psychiatric decisions, etc.).
Conservatorship can be divided in two ways: (1) allowing on parents to make all the decisions—sole managing conservatorship, and (2) allowing both parents to jointly make decisions—joint managing conservatorship. In determining the rights and duties of the parents, the court will decides what is in the “best interest” of the child.