Can the father of my daughter win custody if we have never been married and he dont pay child support. by court?

Recently, I made the decision to move to Texas in July 2010 to look for a better future for me and my simblings. Here in Chicago I dont have opportunities and the cost of living is expensive. My 10 years old girl father doesnt want me to take her with me. He ask me to leave her with him, but I refused the offer. He had never live with us neither have been paying child support by court. He gave money for several years to take care of her, but enough to support her 100%, no even 50. I told him I had always look for my child and that I was never give her away, It is no fair. He told me that if my child say she want to stay with him, he will look for other ways to make that happen. I think he may refer to take me to court. Can he win custody?