
When it comes to splitpushing and splitpushing alone, no one is better at it than Tryndamere. Good waveclear (better with shiv), excellent dueling and tower diving, high survivability when doing it due to his ultimate and his E which lets him go through walls, very fast turret taking due to his build. He has basically everything you'd want in a splitpusher... except the ability to teleport into a team fight and contribute, lol.
If you just want to cheese lane with ignite and splitpush to victory Tryndamere is very good, but if you want a more versatile champion who can still team fight:

All three are very strong picks at the moment and can splitpush well and contribute in team fights.