My baby father wanted an abortion and now wants the baby?

I'm 5 months pregnant,the moment I found out I was pregnant my ex wanted me to perform an abortion, and I refused,,,after some time him and I got into a very heavy argument with him because he didn't want to get a blood test done to test the baby for any disease, I had the nurse called him many times and he got it done...after the argument, I asked him for forgiveness and he told me he needed time to heal from my hateful words,I told him at least to come with me to doctor visits, so he can see the sonograms and he refused because he said he felt hurt and then I should give him space and let him come around on his own, It's been 2 months and I haven't heard from him,I heard rumors about him saying maybe this is not his baby and he is just waiting for the baby to be born and check If it's his. I don't think he will come back duting my pregnancy,I don't think he will sign the birth certificate, he is probably waiting for me to give him updates but he is the father and he should ask me If he wants to know abut the baby's health, he doesnt even know If It's a boy or a girl.,... I have family and friends that support me...sometimes still think he will come back,If he doesnt appear 3 months after the baby is born I think I will start filling for child support... I want to know If I could get full custody rights for me and my baby? and If you have any good advice for me...thank you