His - that was my exact situation when my son was born. My ex was someone I wanted nothing to do with, and I didn't want him around my son, either. Thankfully, he walked away and has never put forth any real effort to be in our lives again. As for the child support, it's my PERSONAL belief, that if someone is not in your lives, you don't have the ethical right to take their money. If the guy is helping raise his child, then he should be helping support the child. I went to court when my son was 4 years old and had the child support order, and the arrears, dismissed. I wanted nothing from my ex, I wanted no ties to him, and I didn't want HIM to have any claim over my son by saying "Well I paid the money, you owe me visitation", or something like that.
I know that not everyone feels that way, and that's fine, I'm not here to argue my stance. But I have been through it, and that's the conclusion I've come to. The way some women and some courts will just relentlessly pursue these absentee dads and suck all they can out of their bank accounts is nothing short of selfish greed, IMHO. I actually had the court mediator try to persuade me to keep chasing my ex, making it sound like it would be fun to take all his money and 'get back' at him; I was disgusted. And my brother, who is now married with a baby girl and living right, is in danger of losing his house and all he has because his ex is suing him for back support, even though he sends her money as often as he can.
I did NOT give my son my ex's last name, because I knew he wouldn't stick around, and I wasn't going to saddle him with that loser's name.
I've told my son about my ex a few times (never anything bad), but he's never been interested in talking about it, and he forgets about it soon after and doesn't bring it up again. His life is full of love and security and happiness, so he's not feeling any absence.
Revenge is never the right thing to do. God can take care of those of us who have been abandoned without us having to go that route.