https://books.google.com/books?id=0...age&q=butler county ohio pawpaw trees&f=false
This Miami Univ tree report on page 39 considers the pawpaw tree a undesirable tree or weed tree and should be removed. No wonder I've never seen any.
On another note I see no buckeye tree here either. There was was one buckeye tree at the corner of my property when I bought the farm but it only lasted couple years and died.