Who has custody of a child if there is no court order?

This one is simple: whichever parent physically has the child with them at that moment. You possess a child because he or she is your child; the concept of custody is something that exists in the law. So, if you don’t live with the child’s other parent, and there is no court order, there is no “custody.” You both have it. Or, more appropriately, neither of you have it.