In New Mexico, like with most states, legal and physical custody can be granted.
Legal custody refers to the parent's authority to participate in the child's life as well as to make the most significant decisions concerning the child's upbringing, education, medical care, travel, and more. New Mexico courts presume that it is the best interest of the child if both parents have equal rights to participate in their child's life unless proven otherwise. So if contact with one of the parents is not recognized as harmful to the child, in most cases, the court tends to award joint legal custody, and parents have to share their rights and responsibilities.
Physical custody determines who provides a home for the child and, therefore, who is responsible for the day-to-day care of the child. Such a parent is called a residential custodian, and the other parent typically gets visitation rights and may spend alternate weekends with the child. However, joint physical custody is also recognized in New Mexico. Such a custody arrangement does not oblige the child to have two homes at the same time or split time between two parents equally. It just means that both parents are ready to spend a significant amount of time with their child, and the courts usually welcome such enthusiasm.