I realize all the discussion on the term child abandonment. In my case I am trying to find out if a father, in the state of Ohio, does not initiate contact with a child for x amount of time, if I can file abandonment so the court can relook at the visitation rights. I am also wondering if in these situations, if Ohio rules paying child support as contact. I have found a lot of information for other states (some which regard child support as contact and other that it doesn't matter if he is paying or not).

You can't file for abandonment. It is not something you file for. If you want to reduce or limit his visitation, you can try going back to court. But the court is likely to say he isn't exercising his rights so why spend the effort to take them away. And yes paying support is considered contact.

You cannot force a parent to exercise his visitation rights. And, as long, as he isn't exercising them a court is unlikely change them.

I guess one issue is, why are you wanting to take away some of his visits, if he is not visiting, he is not using it anyway ? And the court may allow you to reduce his visits, but then he latter could file to get more if he wanted to.

And yes, paying support is considered contact.