Posted twice

If my sons father isn't on the BC and there are no papers anywhere stating that he is legally the father, I don't legally have to let him see our son do I? My son is almost two and I've been letting his dad be here but he would only pop up like once or twice a month and then wouldn't see him again for a month. I know I should've cut him off a long time ago. He hasn't seen his son for three months now (ever since I found out he got his new gf pregnant he quit coming around) and has really never helped financially. The ONLY reason I wanted him here is because I wanted my son to have his father but now I'm thinking it will do more harm than good considering he thinks he can just walk in and out of his child's life whenever. I also recently found out he started smoking marijuana, doing pills, and drinking heavily again. I told him several times if I heard of him doing that kind of stuff again I wouldn't allow him around because I just don't want my son around someone like that. He's already planning on leaving his current girlfriend after that kid is born. Anyways since he's not on the birth certificate or anything like that nor are there papers confirming him as the father I legally don't have to let him around my son do I? I just feel that my baby deserves so much better than this, plus I've given him two years to change for his child and he's actually 10x worse than he was! Also I'm not that worried about him taking me to court and doing a DNA test because he's the type of person that if he had the money for something like that he would end up spending it on something else because he could care less. Also I don't care about child support or anything like that I just want him out of our lives. I've been supporting my son on my own the whole time anyways.