If a father doesn't want anything to do with their child can they sign over their parental rights completely and do they still have to pay child support?
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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Family Law Attorney
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.
Our office schedules phone and office consultations to review cases concerning North Carolina legal issues. This answer does not establish an attorney-client relationship but is a response to a hypothetical scenario and should not be construed as legal advice in your case.