A deputy or the lack of, hardly makes any difference because Mrs May would have picked her deputy, and they would be one of them.
For katkin11, the conservative MPs will vote according to their procedures until there are two candidates left over, then, providing they both wish to continue, the membership gets a vote. If one of them chucks it in then, they don't, afaik.
I just wondered what if neither of them wishes to continue at that point? The can goes on down the road of its own accord, I expect.