A good splitpush champ has 3 abilities.
1- Good turret destroyer (usually AD champs), +1 for those with an ability usable on it (example trundle Q).
2- Great Duelist, so you don't have to flee when someone showing up
3- STRONGER THAN MOST OF CHAMP MID GAME
4- Quick feet, good escape!
number 3 exception fact is Tryndamere the as$hole.
Trynd is definitly the best splitpusher.
Maybe not the best addition to a teamcomp tho, you to see.
Regarding those 4 points, there is A LOT of champs who can do this
You want those 4, or at least MASTER of 3 of them
number 1 and 4 are the most important in my opinion.
number 1, obvious.
number 4, its even better to drag lots of attention then being able to escape, its a big waste of time for more than 1 member to try to catch you up, if you have very quick feet like Nidalee AD, Lee Sin, Twisted Fate, Nocturne, etc. you can join your team very very quickly to make it a 5v4, 5v3 or even worst before they can comeback to help theirs.
Btw Nasus isnt really a splitpusher, he is a powerfarmer sideliner, pain for everybody, selfish useless champ.