There is some additional information on this topic in the current "referrals" thread on this particular
U-haul, so you might want to read that one too.
Short version: It all comes down to your state, and somewhat to the previous state (because yes, if the previous state is an official non-trailer-titling state, you do usually have procedures available in your [titling] state so that you can get a title).
But, as far as I know, NC is a titling state, as is OH, and as far as I know, the new (your) state WILL check that before you can file the "I bought a trailer from a non-titling state and now I want a title" paperwork in your state.