I was with a guy for a month and got pregnant. We had a big argument and we stop seeing each other 2 weeks after I found I was pregnant. He says he doesn't want the baby. He even said he will give up his rights. My question is if he gives up his rights can he be obligated to pay child support still.

First normaly he can't just "give up his rights" and even if the court did allow it, that is just vistis and the such, he will still have to pay child support