Candidates need 1,000 signatures to get their own names on Ohio presidential primaries. Also, they need separate petitions for their candidates for Delegates. The Delegate petitions need 50 signatures within any particular U.S. House district.
Only the Democratic and Republican Parties are currently ballot-qualified in Ohio. Republican presidential candidates who turned in the 1,000-signature petition are: Giuliani, Huckabee, McCain, Paul, Romney, and Thompson. Democrats who turned in the 1,000-signature petition are: Biden, Clinton, Edwards, Kucinich, Obama, and Richardson. This list is not necessarily final. Also, Ohio checks petitions, so just because a candidate submitted a petition is no guarantee that he or she will qualify. Furthermore, not every candidate who submitted the 1,000-signature petition necessarily did U.S. House delegate petitions in each district.
Although Joe Biden withdrew on the evening of January 3, his campaign had already submitted his Ohio statewide petition, so he will probably be on the ballot unless he withdraws. Chris Dodd did not submit a petition; he also withdrew on the evening of January 3.
In the distant past, OH Sec of St would remove candidates that had withdrawn.
I was a candidate for delegate for Jerry Brown in 1980, but his name was removed when he withdrew.
Also, former Sec of State Sherrod Brown (current US Senator) had placed John Glenn on the ballot with out any petitioning in 1984 (the candidates staff had forgotten the deadline), but removed his name when he withdrew.
According to the BoE in Franklin County McCain is not on the ballot as of the Jan 4 deadline.
http://vote.franklincountyohio.gov/boe/