My child turned 18 in January. She is a senior in high school. I have paid child support to child's mother all her life. I have paid this directly with a check. My child moved out of the house and in with a friend on her birthday. I will continue to pay support until she graduates. My question is that my child wants me to give her the money since she is out of the house. Her mother wants me to give it to her. What is the legal thing to do?

What state is this? Most states provide support until 18 and graduated High School. So if that is the law of your state anything after that is a gift.

Do you have court ordered support? If not, you can do whatever you want. If so, then support goes to the custodial parent.