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Singing over rights to your child can be done via a custody order in which the other parent has sole legal and physical custody. If your intent is to eliminate a support obligation that is more complicated. The best way to eliminate the support obligation is if there is another person who will be adopting while you are relinquishing your parental rights. The court wants to ensure if at all possible that all children have two adults responsible for their care and support.
I hope that this information is helpful and wish you the best of luck.