The nuclear family is the most common family arrangement. Single-Parent Household A single-parent family is made up of one person who is responsible for parenting one or more children on their own. While it is possible for two parents to have a single-parent family, it is usually one parent who does not live with their child. For example, a mother would be the single parent of a single-mother household. There are several different forms that a single-parent household can take including: the father only household, the mother only household, and the shared-parent household. In a father only household, there is one parent who has legal custody of the children and lives with them. The parent who does not live with the children may visit them whenever they choose or not at all. If the non-custodial parent has another relationship with one of the children, such as a son-in-law, then he or she may have joint legal custody with the custodial parent. If not, then the non-custodial parent does not have any legal right to make decisions about the children. In a mother only household, there is one parent who has legal custody of the children and lives without them.