Do Ns Care for their Children?

I share a 5-month old child with my ex-N and I am trying to decide whether or not to go NC on him for life. We are not married. He never wanted this baby and throughout my pregnancy vacillated from cheating on me and treating me like crap to going to counseling and wanting to work things out.

He was present at the delivery and stayed with me most of the time while I was in the hospital BUT left the hospital when it was time to sign the birth certificate application. When he returned, he tried making it seem as though it was my fault for him not signing the application. Me being fearful of his rage at the time, told him we'd find another way to get his name on the document since it had already been submitted without his name.

A few weeks later he said we should be a family, so the baby and I moved in with him. Things were great until he returned from his annual skiing trip. After he returned, I started noticing a woman's name popping up on his phone's caller ID. Not only that, he kept stating how he now had to travel out west frequently on "business". Then he began saying that I had to start paying him rent to live there or else we would be evicted. Needless to say, I moved out out of fear of being kicked out at any time because he knew I was experiencing financial difficulties.

Since then, he's been in and out of the picture. His words say that he wants to be in his son's life but his actions say something totally different. He is rarely in town these days because he is seeing the OW, who evidently is an executive with enough cash to fly him in and out of town on a weekly basis. When he does pop up out of the blue, he expects me to stop my life to make his son available to him. However, he still has not looked for a way to establish himself as the father, legally, despite me telling him what he'd have to do and where he'd have to go for the two of us to get his name on the paperwork. I've even noticed that when he doesn't get his way or if I don't stop my life for him whenever he appears, he threatens taking me to court for visitation and then custody but I question whether he will actually do this because he's never in town and whenever I try to contact him (like when his son was sick with croup) he acts like he doesn't care.

Whenever I stopped dealing with him in the past he would start calling me frequently, which he still does to an extent, but I've noticed that since this OW came into the picture, he really could care less but he's quick to give other people the impression that I'm the one keeping him from his child. Two days ago, he told me there was no way we'd ever get back together (which hurt me because I still love him) and that he has the right to see his son whenever he has free time in his schedule and should be given complete access to him, even at his daycare.

My question is: If he doesn't want to establish himself as the legal father and doesn't care about whether his son is sick, then why does he insist on wanting to be in his son's life and does he really care about him? If not, then why doesn't he simply go away and is it right for me to initiate NC when all he wants to do is come in and out of our lives at his convenience?