While being a heavy drinker is not a good thing, you also have to think of the child. Good or bad, this man is the father. That child needs a relationship with its father, unless that man is actually harming the child. No drinking isn't good, but a child needs to know its parents. It can severely mess a child up not knowing who the father is, as they get older. You need to try to have some sort of viable relationship to this person. You liked him enough at one time to get pregnant, so you need to give him a chance to be a father, even if you don't like him. It IS his right, as the father, to have the chance to be one unless he is harming that child. I know you think it's easier and better for you with him gone, but it's not only your choice and it's not only about you now. I think a child also has the right to know who their parents are, even if they aren't good parents, the child should at least know who they are. I am definitely NOT saying this in a rude way at all.

Hopefully in the future you can manage to have civil conversations with the actual father of the child and get along peacefully for that child's sake. It is not okay to cut him out of the child's life because you don't like him. I completely understand about his drinking, but not at least knowing who their real father is and trying to forge some sort of relationship, can really really cause problems for kids as they grow up.

I agree with Johanna's post above too, you and that baby are the #1 priority, but you do need to make allowances for a relationship in the future with the father, if he chooses to want to try to be one.