I wanted to try to see who can get the highest AD in the game. First I tried Yi, because he's one of my old favorites. I got him up to 905 on TT. 5 BT, SotO, Wuju on, Dragon Buff. Then I thought of the other champions who have damage increases that are about that large.
First, I tried Mundo. His E, Masochism, gives 100 AD plus 1 per 1% of health missing. So, that's an extra 199 damage. With Dragon buff, that gives about 235. I did the same build on him, got 1081. (If you don't believe me, look closely at my avatar) I thought this was the highest that was easily obtained, or that I had the patience to do.
Sion, however, has no cap to his damage. If you get Bloodthirsters and a Tiamat (to farm quickly, then trade it out) plus an Atma's Impaler, you can get literally infinite damage. I made it to about 700 damage (this was on SR) when I got bored out of my mind.
If anyone actually took the time to get higher AD than that, please tell me, I'll have to try it.