How do the effects from multiple Tiamats stack?
Solution 1:
The damage stacks additively, so with 3 Tiamats you will be dealing 150% AOE damage. Meaning you are dealing MORE damage to surrounding targets than to your initial target.
For your amusement, here is a video of caitlyn stacking 3 Tiamats. You can see the surrounding champions take 216(ish) damage 3 times, once for each Tiamat.
Solution 2:
Tiamats will stack additively, meaning each Tiamat will deal 50% splash for melee attacks or 35% splash for ranged attacks. With 6 Tiamats, you can do an extra 300% splash damage with melee and/or 210% extra splash damage with ranged attacks. The radius of this splash damage is fairly small (185, only slightly larger than the range of Singed's Fling attack).
The splash damage does not confer additional benefits, such as life steal or chance to critical hit, although bonus damage if the original hit was a critical will still transfer into the % based damage.
Do note that the splash only applies to default attacks or attacks that proc on-next-hit effects such as Ezreal's Mystic Shot, Warwick's Infinite Duress, Gangplank's Parrrley, or Fiora's Blade Waltz.
Tiamat is generally considered underpowered due to the fact that it's overall benefit is very minor compared to the cost effectiveness of what you could be getting for a similar price. Additionally, it is the only item in the game that builds directly out of 4 basic items, making it one of the hardest items to plan for in regards to inventory management.
Solution 3:
The LoL Wiki says:
- The splash damage passive from the item is not unique, meaning that it is possible to obtain up to 300% splash damage with 6 Tiamats.
- The bonus splash damage of each Tiamat is dealt separately.
The answer is, yes you would be dealing 150% of your damage to sourrounding units/champions. But, the cost of the item is pretty high for what it is worth, and if you are building 3 tiamats your damage won't even be that high...You might as well just build one and beef up your base damage. Also unless you are playing with total noobs, your enemies won't be bunched up enough for you to really get more than 2 chamions in one splash.