A domestic violence conviction makes one removable from the U.S. However, if your conviction was reversed on appeal, you have nothing to worry about.
With all due respect to Mr. Shusterman, a garden variety domestic violence in the state of Ohio is not necessarily a deportable offense. Last year we won a case in the Cleveland Immigration Court where the judge agreed with our position; the statute of conviction does not contain an essential element of force (necessary pursuant to Leocal v. Ashcroft). Since our victory, two other attorneys have used our brief and that decision and have received the same result. That said, these victories have not deterred USCIS and ICE from charging people and putting them in removal proceedings. You should retain counsel from this point forward to ensure your rights are properly accorded you.