I'll try and explain my situation as quickly as possible. I was with my partner for over a year when I fell pregnant, he was always jealous possessive and very volatile.
When I fell pregnant his words were ' haha you can't run off now'. Then said 'i don't think so' when we discussed him doing night feeds etc. He also refused to spend his money on any baby items.
He is a very heavy drinker and was drinking until he was mortal every night, after an argument one night I went to stay at my parents to avoid further conflict (I as 7 weeks pregnant). When he returned from drinking he came to my parents house and began trying to kick the doors down to get at me, and even tried to knock my mother out the way to get into her house. I'm pretty sure he tried to hit her as well but missed. We rang the police but he had left before they arrived. When I went back the next day he had smashed my things up.
We split but I agreed to give it another go if he stopped drinking and went for anger management. He did neither. He then began sending suicide threats, saying he may as well kill himself if I wouldn't go back to him. Then began sending abusive messages calling me and my family all sorts of names. I had to move back with my parents and cut off all contact with him.
He left me alone until last week in which he posted a status on Facebook threatening me if I did not give him the child when it was born, again police were called but he said he never meant it to be a threat and just meant he was going for custody. (Police agreed it did look like a threat)
He has been warned to leave me alone and police advised i take out an injunction against him. I know he has attacked and injured his own father (and countless other people) and past girlfriends have also submitted statements about him being violent with them.
The baby is due any day and obviously there's no way I'm letting my child go to anybody like that. I've sat and cried worrying about the trouble he will cause trying to get access to the child I believe he doesn't want anyway.
I have been told my somebody that if I refuse to have him on the birth certificate he has no rights to the child. And even if he applies for PR through the courts he still cannot have access unless I agree to it.
Is this true?
I'm really worried over the safety of my baby is he gets access to it 
Thanks in advance.