Ok, I will tell you what I know from my meeting with a solicitor.
Although in your case he is on the BC, he would have to prove he's earnt the parental rights the BC gives him to a judge in court if you contest that he hasn't been there. So he has to state everything he has done to be a good dad....in his case nothing.
He would probably be granted contact, but there is no way that will be allowed with is girlfriend. If they stayed together for a year or two only then if they went back to court would a judge maybe give them access away from you but your LO would be much older by then, at 4 I would say.
No overnight access either "for a long time yet" was what my solicitor told me....probably at least 3/4 yrs old.
All parental rights means is he can have a say in schools, medical treatment etc. If he hasn't done nothing for your son and you can beyond doubt prove that then he will be given no more rights than someone who isn't on the BC.
My ex threatened me with court and solicitors. I think he thought he would scare me into giving in to his demands. When he found out i'd seen a solicitor he soon backed down and that's because I know he was told by his solicitor he would have more chance of trying to sort it out with me than going through court. We managed to sort it but he's just effed it up again so I don't know where this will leave us now.
You have every right to stipulate visitation at your house with you present at what times suit you and your LO. I do and that's not going to change until LO is at least 4. x
I live really close to town so he sees it as convenient to come and harrass me. Scary thought that his rights are the same as mine though 
Rights should be earned...
