If both you and the custodial parent agree, then you can have your parental rights terminated, and you will no longer be responsible for any future child support payments. You will also no longer have any rights to visit with the child at issue, or make any decisions regarding his/her future. Your past child support arrearages, however, will still be due to the custodial parent. There are a number of ways to deal with an outstanding child support award, but you will need the custodial parent's cooperation in handling the issue. I urge you to speak to an attorney for a free consultation to discuss your options further.