Some parents aren't married. They chose to live together without getting married. In legal terms, this is called a “common law” relationship.
When common-law parents stop living together, they don't have to get a divorce, because there is no marriage to end. But they do need to decide what will happen to their kids and how they will divide their property.
The laws about parenting are the same for married couples as they are for common-law couples. Parents need to decide on living arrangements for the kids and to decide on visitation schedules, so that the kids have the opportunity to spend time with both parents.