No. Courts frequently award at least partial custody to both parents, called "joint custody." Joint custody takes one of three forms:
In some states, including New Mexico and New Hampshire, courts are required to award joint custody, except where the children's best interests -- or a parent's health or safety -- would be compromised. Many other states expressly allow courts to order joint custody, even if one parent objects to such an arrangement. For more information, see Types of Child Custody.