If my ex is sending me papers to sign over my legal rights to my child, am i still obligated to pay child support?

You're right - it is different - in New Jersey you can certainly give up your rights as a parent, but you will still be oblikgated to pay child support.  Even if your ex says no - you will still be obligated.  If you don't pay, your child has the right to come back after you when he or she turns 18.   A parent cannot waive child support on behalf of the child.