There are several types of custody: joint, sole, shared and split custody. They are explained below.
Generally speaking, judges in New Mexico prefer to award joint custody in cases in which the parents agree that they can consult with one another in order to make joint decisions on major health, education and religious issues on behalf of a child. It does not mean that either parent can come over to the other parent's home and have the child whenever he or she wants, or have the child half of the time. There is still a basic parenting schedule that is to be adhered to unless mutually agreed to the contrary (e.g. swapping a weekend here or there, changing weekday visits and having the child for special occasions, etc.). One parent is designated the primary residential parent, and the other parent generally has the same child support obligation as in sole custody situations. When joint custodians disagree on an issue, they have to first try to resolve it with a mediator before litigating.
This form of custody may be appropriate where there is a serious breakdown of communication between the parties, the parties live quite a distance from one another, or the non-custodial parent has demonstrated an unwillingness or inability to competently and consistently parent. Even in these situations, however, the non-custodial parent is entitled to reasonable visitation and notification of grades and health problems of a child. That parent can also generally attend parent/teacher conferences and observe extra-curricular activities of the child (e.g. a school play that does not fall on a regularly-scheduled visitation night of the non-custodial parent). Sole custody does not terminate the parental rights of the non-custodial parent, which is typically a non-divorce related procedure pursued by the state's attorney's office in the event of serious neglect or abuse to a minor. Sole custody also means that if there is a major health, education, or religious issue, the sole custodian may make that decision without consulting with the other parent.
This is more or less the Solomon (split the baby) approach to child rearing. An example would be where the children alternate each week between each parent's home (sometimes the children stay in one home and it is the parents whom alternate residing in the home). Generally, a judge will not award this type of custody unless the parties freely agree to it because some opponents of it say it treats the children like luggage. A more acceptable form of this custodial approach is to perhaps reverse the school parenting schedule with the summer parenting schedule. There may still be a child support obligation of one parent to the other even in a 50/50 visitation situation unless the parties have relatively similar incomes and assets, and they freely and voluntarily agree to this form of arrangement.
This is typically where one child lives primarily with the mother and the other child lives primarily with the father. This is not favored by courts, as generally it is better when the siblings live together during the week as well as the weekends. But there are cases where there are serious problems or age differences between the siblings, or one child has formed a strong alliance with one of the parents. Usually a guardian ad litem or a child representative is appointed in these cases so the judge is confident the arrangement is what is best in the situation. Child support is an obligation of both parents, so sometimes the mother in this situation will pay child support to the father for the child he has, and vice-versa, or the respective support obligations are offset with the higher income-earning spouse simply paying the difference of the parties' respective support obligations to the lesser-earning spouse.