My son has a 2 week old boy. Both parents hate each other. Only had casual relationship before baby born. If he gives up his paternal rights is he obligated to pay child support.

Sure he is. He doesn't have to see the child if he doesn't want to but he's going to pay and keep on paying.

If somehow they allowed him to give up his rights ( which is very unlikely) he will have to pay child support unless the girl gets married and they want to adopt.

Also he does not have to ask for any "rights' so he does not have to file for visits, he does not have to ask for anything, he merely has to pay support for 18 plus years.

His "casual" relationship ended up in a child, now he has a legal and moral duty. I am disapointed that a parent would seem to not want to teach their child being responsible.