Family Law Questions? Ask a Family Lawyer Online.
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You have no rights until the child is born essentially because you cannot legally prove that the child is actually yours. Thus, you can't really do anything until the child is born, and at that time, you can file a petition in court to establish paternity (DNA test) and then seek to have your name placed on the birth certificate, give the child your last name, establish visitation, etc.
However, you unfortunately cannot take much action until the child is born.