Who gets custudy of my little half brother if my mom is committed to rehab. His father hasn't been around, paid support and is an ex convict, abusive alcoholic. I'm the oldest child and my mother wants him with me but she never put anything legally in writing that I know of.

The court will look at your age and your ability to provide for your brother.

As great as wanting to take care of him it is not enough in the eyes of the court.

You must be stable, working and able to provide,have no criminal background.You must be 18. You would have to present to the court why you would be the best person to care for your brother.
I wish you the best!

EDIT: since I reread and saw half brother,the father would have precedence over you ,if you think he is not capable and you are ,you can ask for custody.Your mother has a say even if she is in rehab. She can appoint you guardian if you qualify for guardianship.