I contacted my son's (non-abusive, yet still a twat) father earlier in the year.
DS had felt unsettled since starting school being the only child without a man to call dad, especially as the children with parents that have broken up have a dad somewhere and see him at weekends/after school. I also wondered if it would help his sense of identity to meet and know him.
I felt that I no longer felt threatened to have him involved rather than the scared feeling that I had experience previously that he would one day demand to see his son who I'd brought up for the last x amount of years.
Anyway, I contacted him and arranged to meet up. He has no money and so it wasn't about financial contributions and I didn't want to immediately give him rights over my son who has "Father: unknown" on his birth certificate.
When the day approached, I received a charming text message (as we had corresponded via text) telling me to go via the CSA and make a disputed parentage claim and that he would like DNA tests (which he knows that I won't do). It was another lucky escape because I remembered what sort of a controlling, narcissist man he is and that we really are better without him.
He's not a child, a 47 year old man, and it's clear as crystal that he wants nothing to do with my son. Case closed for me. Told DS that he's still not ready to be a dad and that he's too busy.
We didn't really discuss it much until DS told me that the real reason that he wants a dad is to have shoulder rides - so I have a friend that gives him one around once a week - he seems happy enough now 
You see the bottom line is that if having this man in your life would make you stressed or anything but the calm, happy person that you and DS need, then having him involved is not in your best interests.
I'm really looking forward to the "I want to live with my dad" rants in those delightful teen years!