To do this you would have to have a judge order the termination of parental rights after a hearing to determine that the father was doing so knowingly and wilfully. You can also have the judge give full custody to the mother and still require the father to pay child support. You should not attempt to do this without the assistance of an attorney.
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A father can voluntary relinquish his parental rights through an adoption proceeding, e.g. if the child's mother remarries and her husband wants to adopt the child in a step-parent adoption or the father's rights can be termination if you file a Petition for Termination of Parental Rights.
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