Who has the rights to the child when there is no court order?

If the parents are married they have equal parental rights.

Generally, if the parents are unmarried the mother has sole custody and control in most states until the father can establish his paternity. Remember, a child's mother can always be identified by medical records. Since the father didn't give birth and he was not legally married at the time of the birth he can establish his paternity through a DNA test. A paternity test can be arranged through the court. Once paternity is established in court, the father can request visitations or custody through the court. If the mother retains physical custody she can request that the court issue a child support order. If the father gets physical custody he can request a child support order.