I am in the military. My home state is Texas. A girl got pregnant and baby is due in November. I am not sure it is mine and won't be certain until baby is born and DNA is done. My question is: Since my home is in Texas, if I relinquish my right to the baby, do Texas or North Carolina laws rule if the child turns out to be mine? Her home is Florida. Trying to assertain if I will have to pay child support under North Carolina law if my home is in Texas and hers in Florida.

Does not matter where you are a resident at, the state where the mother and child reside is the state where the child support and custody will be dealt with.

And no idea where you think you can "relinquish" your rights? You can not apply for any rights and let mother have full custody and you don't have to ask for visits.

You will have obligation, child support and perhaps medical coverage and other care to pay for. That is a obligation not a "right" and you can not sign them away.