“My question is: can I sign over my paternal rights to avoid paying child support? If my child lives in North Carolina and I live in New York, how would the amount that I am responsible to pay be determined?”
You can’t just sign over your rights in some informal way. If you file a Petition for termination of parental rights, the Court in North Carolina will determine whether by clear and convincing evidence termination of your rights is best for your child. Some of the grounds are: Abuse, neglect, child in foster care for more than a year, DSS involvement, failure to support (and termination in the child’s best interests), incapacity of the parent, etc. If the Court does not terminate your rights, support will likely be by the guidelines of the state where the request to determine support was filed.