Hi and thanks for your question.
You have a very strong argument to have sole physical custody/parental rights to your child with supervised visitation of dad with child, if any. The court should see that in light of all of these factors, your child would be in potential danger if left alone with father and that visits with dad are not in child's best interest.
The court will not extinguish his parental financial obligations for the child unless there is a pending adoption. This doesn't mean that his parental rights to visit and make decisions about the child cannot be terminated or at least significantly restricted in the best interest of your son.
I hope this answered your question; if I have answered your question, please click the green Accept button. Thanks very much and I wish you the best of luck with this.
If there is going to be an adoption, and if the biological father hasn't paid child support in a year or had communication with your son for a year, then you may be successful.
Here's a sample of the Petition for Adoption of a Minor Child in Ohio - I'm not sure if this is your county, but it will give you a sense of the information needed for the process.
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