Pick a champion for base stats and melee/ranged
Pick Passive and Q/W/E/R abilities (Ex: A Q from a list of all Qs, if you are ranged you can pick from all ranged champion Qs and vice versa.)
Have a great time with your new champion for a game!
Possible additional rules
Banning certain champions or abilities
Removing some abilities due to incompatibility
Less turret health for shorter games
Showing all abilities in loading screen
While this would be fun it would be very difficult to implement. Animations for each skill would have to be made for every champion capable of using it.
Caitlyn Base-For range(650) Tristana Passive-126 range at 18 Jinx Q-175 range at max rank Kog Maw W-210 range at max rank Kayle E-400 range Twitch Ult-300 range For a total of 1861 range with all abilities activated. Sounds like fun!
All of the stacking. All of it
P 
Q 
W 
E 
R 
I think you'd have to have some passives ONLY available to certain champs (Gnar, anivia, zac, sion)
OTHERWISE Heres what i'd do:
Champion: Jax Passive: Aatrox's Passive Q: Riven's Q W: Vlad's W E: Fizz's E R: Kayle's Ult
Passive: Katarina Q: Morgana W: Tristana E: Kayle R: Akali
There, I just broke the game.
This champion and desired abilities. QWER =
ult.
I'd just pick Swain with anivia's passive.
Dota 2 has something like this, certain heroes are disabled though due to their skills needing another skill, and everyone gets a random hero and they take turns picking from a pool of the heroes abilities, 3 basic skills and a ult. If this game mode would happen mana champions would be the ones available. Karma, Tristana, and a few others wouldn't be in it. Stamina, rage, well, no resource, and metal shield thing champions wouldn't be available due to obvious conflicts. You can really see the most obnoxious combo's going around though and making the game mode short lived.
In my opinion would only work if the champions and abilities thrown into the pool were randomized rather than picked by the player, otherwise you would see the same things nearly every game.
This thread made me go play DotA.
Kat Passive + Anyone elses ult = GG
P
Q W
E
R
Udyr, but with Malzahar's passive. Hide your turrets.
they do it in dota, cant see why they dont do it in league!
I shall pick Caitlin's bases. P: Braum's Concussive Blows Q: Draven's Spinning Axe W: Vayne's Silver Bolts E: Kayle's Righteous Fury R: Jax's Grandmaster's Might
So at level 18, that's doing 185% of AD on attacks plus 60 (+25%AP) magic damage- in 1050 range (Just a little bit less than vision range-about 1200). Every third hit does 60(+8% max HP) true damage plus 220 (+70% AP) magic damage. After 4 hits, the target is stunned for 1.75 seconds, taking 176 magic damage. Attacks thereafter for a few seconds deal an additional 35 extra magic damage.
Oh and they have an armor/mr steroid (meh.)
Assuming 2 attacks/second attackspeed, 500 AD, and a target's max hp being 2000, 100 armor and MR: 1 attack 925/2 + 60/2 = 492.5 damage 1 second = 985 damage 2 seconds = (9852) + 220/2 + 60+(.082000=160) +176/2 = 2378 Damage (Dead)
This would really need some limitations on the picking mechanic as we see from all of the people theory crafting below. If it were to be implemented, Riot should borrow (Read: steal) how the system works in Dota 2. That would mean you're given a random champion and then you get to pick draft style from only abilities of champs selected + a random amount of other champs abilities (Just so there's extra abilities left over).
Doing this is necessary because people pointed out below, it just becomes an OP fest if you don't have this.
's passive
's Q
's W
's E
's R
with 
for base stats and range
Lol did you copy the phrase i used in my instant battle mode? :'D
Passive: kalista passive Q: fizz q W: zed w E: ezreal e R: kass r
Or Passive:eve passive Q: shaco q W:wukong clone E: any ability (can't think of a stealth that is on a w) R: rengar ult
Enjoy your freelo
