I receive child support for my three year old child. Her father resides in Trumbull County , Warren, Ohio. He pays child support. He does not want to be involved in her life AT ALL and will only pay the child support. I need sole custody because I reside 10 hours away and will be applying for a passport for her and other things which the other parent is required to sign for. How do I retrieve the legal court forms for him to sign and we can submit to the court? What is the process? He is not willing to attend a court hearing but will sign for me to have sole custody.

Sincerely,
Getting on with my life

Why won't he sign the documents needed so his child can get a passport? If your custody situation is court ordered then you will have to file with the courts to change it. Court can not be avoided for a custody change.
Also you state you are 10 hours away. Did you move or did he? If it was you and he still lives in the area of the original court custody order then you will have to file in that court.

First sole custody does not mean that the father does not have any rights, and he can not just sign his rights away.

And there is no way at all to get custody changed without going to court, there is no papers just to fill out.