Another possibility is someone with global pressure. Shen is a great split pusher.
Why? his attack speed sucks, his base damage sucks, his wave clear sucks.....
But if while you're split pushing, a team fight breaks out, you can ulti in and be right back into a 5v5. So you're able to maintain 5v5 pressure in say, midlane, cause of the threat of your ulti, so you get either a free 1v0 push, or enemy is forced to 4v4, which can quickly turn 5v4 in your favor.
There's other champs like this too.


all hold some form of global pressure. (and
, but FK Teemo! =P )
I'm not saying you should always split push with them, just something to think about, even if they're not with the team, they still have something to offer to a team fight should the enemy force one.
But also, those champs need to keep in mind their global pressure and be ready to use it even while splitting. Shen ulti's not gonna help if you wait till 3 guys die before you notice and use it.
Also stealth champs are nice, you can kind of bluff and enemy into thinking you're 5v5 mid, so they're scared to engage. Then your stealth slips off and gets a tower before they have time to react. You gotta be careful with that one though, cause you need to let your team know when you're gonna reveal yourself so they have time to back off so enemy doesn't realize you're not there, then collapse on your allies because they see you're not with the team anymore.
But yes, lacking that, whoever has the best waveclear and escape mechanic should probably do the split. Coughcough cough
Also, timing on your splits matter a lot more than who splits. If dragon's up in 30 seconds and you're blue side jungler and you wanna push top...don't. You're gonna force allies to contest dragon 4v5 without smite. Likely even if you get a tower in your split, you still cost your team some pretty heavy losses you could have prevented by being there for dragon, then do your split after.