Which champion would win a Free-For-All in Summoner's Rift?

As a preface, I will say that I understand that all champions have a (few) "counter-champion(s)". To end the argument that it would be at random because the champions will defeat each other in a circularity, one must note that some champions will be able to take themselves out of this (not so) endless loop. Now to set some conditions by which this will happen:

1. All champions are in their level 18 state
2. All champions will be built to optimize their fighting capabilities. (Ex. Ryze would have Fully Stacked Rod of Ages, Sorcerer's Boots, Seraph's Embrace, etc.)
3. All monsters in the Jungle will be a non-factor. No buffs will be obtained through slaying them.
4. Turrets are disabled. Additionally, minions are also disabled.
5. It is to be assumed that cooldown times on their abilities either don't exist or they only make a negligible difference.
6. Though this may be obvious, I felt that it was necessary to include the fact that champions can buff/debuff enemy champions at their own discretion.
7. Maybe Amumu will finally make a friend.

PLEASE take into account what everyone else has said before posting an answer. It will only help further the discussion if you use others' logic in order to make a solid conclusion. Also look at the lore for each champion, as it will provide interesting "food for thought" that can also help further the discussion in a meaningful way.

To conclude, I will give my own answer. I think Zilean would rip everyone to shreds. His chrono-displasia left his mind (empathy) detached from his body (survival instinct). Because of that, his body (which would obviously be in the fight, rather than his mind) would be bent on its own survival, instead of CARING about the needs of others. Additionally, he can control time. Pretty solid win in my book.