[2021] Build me the most broken champ you can think of using the current characters’ abilities

• Base stats: Ashe or Caitlyn (Range, base DPS)
• Passive: Nautilus. Root everyone on first attack? Get me in there.
• Q: Tryndamere. Infinite sustain, plenty of bonus stats.
• W: Lee Sin. Solid escape tools, really high sustain as well.
• E: Gwen. Escape if needed, plus great damage output
• R: Olaf. Passive resists are good if you just want to make sure there's no way you die to a Katarina/Talon or whatever, while losing those stats for AD and unstoppable works really well, too.

E or Q max. W is an OK one-point wonder.

Tryndamere one is a good point but 10-30 AD and a "press button to heal for 30" isn't trash, either.

Lee Sin I think it pretty forgivable, but I see it.

A new one I thought of, probably the best self-sufficient marksman one could make:

• Caitlyn base for the 650 range and solid base stats otherwise.
• Passive: Taric. Every ability grants 2x attack speed autos that refresh ultimately provide -2 to base cooldowns.
• Q: Vayne. Tumble's base cooldown is 4-2, making it very easy around rank 3 to tumble, 2-auto, tumble forever.
• W: Kog'Maw. Bio-Arcane Barrage is the best auto-attack steroid I can think of for this kit. Bonus points to the fact that it'll always be up thanks to Q+Passive.
• E: Pyke. I think Phantom Undertow is the best self-peel tool available in League. Solid range. Stuns your pursuers. The base cooldown of 15-11 should be fairly easy to get back with the Passive/Q interactions.
• R: Master Yi, Nasus, maybe Alistar.
• Nasus's Fury of the Sands grants 40/55/70 armor+mr and 300/450/600 health. The damage around you is irrelevant, the half cooldown Q doesn't apply (it lists Siphoning Strike) but doesn't matter. You shouldn't need any more damage, so why not just survive a Talon or Zed all-in?
• Highlander grants 25/45/65% AS and 35/45/55% move speed, which is also great, but I'm not sure more damage is needed. The resets for the high duration are valuable, though.
• Unbreakable Will is probably just the strongest option though (and comes in post-edit). 55/65/75% damage reduction and an instant cleanse is probably just the best survival ultimate out there. The duration is under half of Nasus's ultimate, but the short-term durability is almost always higher.

Taric-passive kits are probably a cornerstone for a lot of broken builds. Maybe there are better instant-cast short-cd abilities that are better here.

Could be, but I'm putting value in the instant application.

Naturally