Some parents aren't married. They chose to live together without getting married. This is sometimes referred to as 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 custody and access are the same for married couples as they are for common-law couples. Parents need to decide on living arrangements for the kids and access rights, so that both parents have the opportunity to spend time with the kids.