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Since she is still pregnant she is free to go anywhere she pleases. Once she has the child she is more restricted since the father can petition the courts to bring the child back. If she plans on leaving before having the child is her top choice.
He has the same rights as she has.......he can not be forced to sign away his rights and even if she can talk him into it the courts often deny these petitions unless the child is being adopted by her new husband or it is in the child's best interest. Once the child is born he can petition for visitation or custody of the child and she can petition for child support. Since they are unmarried she has automatic custody of the child.