I prefer the baby daddy out of her life..

Chai • Growing everyday with my baby daughter 💗
I would really love someones opinion on this. I'm having a really hard tome coping with this by myself. My mom is very supportive but I would just like someone else to look at the situation. 
First of all I'd like to ask for anyone who disagrees not to bring their comments in a hurtful way, because I already lost my best friend in the process of this situation and I have been crying and feeling quite alone and depressed all they, even though I'm trying really hard not to, because I know my little nugget will feel that. 
When I found out I was pregnant, it wasn't really happy and rainbows. It wasn't planned because I'm just 16 and my boyfriend was 20. After a while I decided to break up for the best, because he was very immature about the whole thing, demanding my parents to accept the situation, not understanding why they'd prefer me to have an abortion or put the baby up for adoption, thinking he could make enough money (as a dishwasher) for keep himself me and a baby alive and have us move in with him (while he still lives with mother in a three room appartment while she hates me and demanded to abort the baby) .. Among other things (like his mother payed three studies for him which he didn't finish all three and prefered staying at home smoking weed all day) this made me realise he was never going to be a good father, and he was also just thinking about himself. He couldn't live with an abortion, etc. 
Now I still live with my parents, I work and I study, and my parents have accepted the situation, happy he is not around as well anymore, and they are willing to help with the money a lot. So my daughter will have a really good life among lots of people who love her and can provide her with everything. Meanwhile I'm working on being a lawyer. 
I told my ex that I think he will be nothing but a bad influence on my daughter (I can't say 'our'. It just makes me sick.) and I would want him not in her life at all if possible, but I accepted some time ago that it wouldn't be possible because I couldn't make that decision for her. I wanted her to know who her father was so that in time she could choose for herself if she wanted him in her life. He would get to see her a couple of times a month. Also I wasn't planning on registering him as her father on paper, because where I live that would give him a lot of rights. I just don't want her not to know her dad, if that's just gonna happen I don't see why he would need to be registered as her father. This would mean I wouldn't be able to travel with her ever without his permission and he would have to attend a lot of events such as making her passport etc. Unnecessary headaches for me. 
But today we had a fight, and I don't know weather to stick to the plan above, or move out of the country closer to my family in Brazil, so I'd have more support and less stress/pain he is causing me. He is stalking me on facebook, wanting to know what I'm doing through my friends their statuses I'm tagged in, etc. My best friend doesn't  understand the situation at all and doesn't get why I can't just 'accept he is the father and deal with him' and just be nice. Anyone can be a sperm donor and make a baby. It takes a whole lot more to be a FATHER. 
I'm sorry but I can't be happy with a boy that is claiming  wanting to be a father (while his only argument is not wanting to know his daughter is walking somewhere not holding hands with him) while he doesn't even have a house, an income, an education other than a highschool diploma, and his own friends (the ones he does have even worse jobs and smoke weed all day). I don't want my daughter to grow up without a dad somewhere (I don't think you NEED a dad. I know lots of people that grew up without and they turned out fine.) but I also don't want her to grow up with a dad (who in her eyes will be really important to her) that is such a bad influence and will be a terrible mirror in her life! I mean, if he grew up with good parents and turned out this way, how will someone with shitty parents grow up to be? I don't want her exposed to that! Is this so wrong?