The laws of most states are designed with the assumption in mind that a baby's parents are legally married. This can raise questions in some cases where the father's name is not on the baby's birth certificate. For mothers in Texas, they may think they have to file for custody or that it might be a bad idea to file if it causes a father who was out of the picture to show back up to make demands for joint custody.
In some states, the law presumes that a mother has only initial custody, rather than sole custody, even if the father's name is not on the birth certificate. The birth certificate generally does not establish paternity; the father may need to establish paternity before his name is put on the child's birth certificate.
In other states, the law presumes the mother has sole custody. If the parents are not married at the time the child is born, the father in one of these states must prove paternity, and the judge can issue an order to change the child custody arrangement. The court will generally give the mother and the father each an opportunity to prove that changing custody is in the best interest of the child. This is true even in cases where the child has been living with his or her mother prior to proceedings.
For people who have questions about the operation of Texas law on situations like this, it might be wise to speak with a lawyer. A lawyer with experience practicing family or divorce law may be able to help by examining the facts of the situation and developing a strategy for custody proceedings. A lawyer might argue on behalf of the client during hearings or attempt to reach an agreement with the other parent.