The problem with the question is we have a state by state answer as to what happens during a contested convention.
Assuming Kasich drops for whatever reason and another candidate gets to 1,237 then nothing really happens that matters. That candidate is the nominee, assuming no extraordinary shenanigans at the convention by GOP leadership (establishment.)
But... assuming Kasich drops (or does not drop) and no candidate has the magic 1,237 number then the convention goes to contested rules.
At the GOP convention there will be rounds of delegate voting. Most of the states requite that during the first round the bound delegates vote as it happened during the primary process (i.e. stay with the original candidate no matter if they dropped or are still active.) Once that happens and no one still has the magic number, then the backroom deals take over. It becomes "brokered" per rules of the convention (which are all subject to change by some of those same delegates by "rules committee" voting.) Some states still require their bound delegates or a percentage of them to vote as they did during the primary no matter how many rounds of contested voting occur, others though allow some or all of those bound delegates to change their vote. Either post round one or round two (I forget which) almost half of the bound delegates basically become unbound and can vote for anyone they want. Including someone not even active in the primary. Brokering takes over and you have a fair number of delegates that basically switch to some other candidate to the point of obtaining the magic number in some later round of voting.
As I mentioned above the rules committee for the GOP is extremely powerful, and can upset this at anytime. There is basically no way to know who will end up on the rules committee per convention as some of the states have not even elected who their representative will be for that committee. Because of that, we have no idea how prone they will be to making a rules change because of a brokered convention that goes off the rails. For instance... if Trump does not get to 1,237, no one else does either, the GOP looks to hand the nomination to whoever, and Trump throws a fit at the convention about it. Odds are the rules committee would have to step in just to engineer a path to some brokered deal.
During a contested convention then the states of Pennsylvania, Massachusetts, Kentucky, Main, Ohio, Colorado, Wyoming, New Hampshire and Michigan will become more important. They will have the most delegates that are free to vote for whoever they want to anyway, or become able to do so quickly during a brokered convention (post the first round.) New Hampshire and Michigan especially as the moment a candidate drops out, even before the convention, those bound delegates become automatic unbound delegates. Before a brokered convention is even declared. To make matters even more interesting, the bound Massachusetts are still attached to Kasich until he himself releases them.
You asked about Ohio. Those bound delegates are still bound to Kasich through the first round of voting at the convention even if he drops. After that, we have a rules problem from Ohio. Best I can tell there is no rule about what happens when a candidate withdraws or suspends. So, enter the rules committee is our best guess. I agree the winner take all makes it interesting, but the absence of rules on this makes it worse. They do not automatically go to anyone best I can tell, nor to they automatically go unbound like the other listed states.
The one thing to keep in mind is this is not some governmental process with laws in control, these are establishment political parties that damn near get to make up the rules as they go along to ensure this outcome or that. And, they can change the rules as they see fit.
I am thinking if it comes down to the wire and Trump is a few delegates shy,
he may start courting for a VP (who has a few delegates) both Kasich and Rubio are possibles.