what i would suggest you do is cut contact with this a$$hole, change your number, change your address, and don't tell him when the baby is born and definately DO NOT put him on the birth certificate.
oh and as for him thinking he will get custody from birth, um i'm thinking maybe he's got a few too many birds on his antena! my ex tried to threaten me with **** like that too, he said he would get a court order to be present at the birth! YEAH RIGHT, like anyone in their right mind would give that right to any man! even a man judge wouldnt let him do that!
but yeah, i cut contact with the ex when i was 5 months pregnant and i'm tellin ya it was the best damn decision i ever made, i never changed my number tho, i moved interstate(which he already knew about) but he didnt know exactly where i was going so he'll never be able to find me, and as for my phone number, i just ignored all his calls and messages and eventually he just gave up because he had no other way of contacting me.

i just hope for your sake that this guy comes to his senses and realises that its YOUR baby, not his. a mother will always have more rights than a father, i have a lot of family friends etc who were very decent men and still had trouble getting any kind of custody of their children, in one case, my friend's ex wife was a complete nutcase, and it had been proven in court, and she still got custody of his son! so if that helps, i'm pretty sure you're not phsyco, and you're capable of taking car of a child (duh), so no judge will take you're son off you.
and if you can, dont put his name on the birth certificate because technically, if he's not named as the father, then he has absolutely NO RIGHTS to you or your child whatsoever, and that'll make it so much harder for him which is what we want! make him cry!