The only Star Trek splitting story-line that I recall [1] was not actually resolved! Lt. Riker just sort of disappeared into the background at the end of the episode, with Cdr. Riker and the writers never mentioning him again.
EDIT: apparently Lt. Riker showed up in a DS9 episode[2]!
Sort of both resolved and not resolved since I can't remember him coming back. It did give Frakes an opportunity to play a different character later on in DS9.
I liked that episode and would have enjoyed Thomas Riker showing up again from time to time. Although it was another one of those "why can't they just restore dead crew from the transporter beam?" episodes. Even worse than the Scotty one since doubling Riker means that Riker's matter didn't really matter much.
EDIT: apparently Lt. Riker showed up in a DS9 episode[2]!
1 - https://en.wikipedia.org/wiki/Second_Chances_(Star_Trek:_The...
2 - https://en.wikipedia.org/wiki/Defiant_(Star_Trek:_Deep_Space...