Katarina's ultimate, Death Lotus is a channeled ability (as you may notice in the cast bar that appears and counts down). Like any other channeled ability, taking any other action, such as using an item like Zhonya's Hourglass, will interrupt the channel.
Other Champions, for instance, Fiddlesticks, Kennen, or Morganna, don't need to channel to maintain their ultimate, meaning Zhonya's can be used to safely shield them for its duration.
Accurate as of May 2013
Aegis of the Legion is a very cost-effective item, and it now upgrades into Runic Bulwark, which is slightly less cost-effective, but provides more statistics. For just the item owner, with the aura hitting no allies, Aegis is 107.32% gold efficient, and Bulwark is 96.56% gold efficient
.
Below is the math, in terms of gold efficiency. I've used the cheapest items available for each statistic to calculate the equivalent gold value of the final item. Obviously if you're comparing against more expensive (and usually more efficient) items, the gold efficiency of the Aegis and Bulwark will fall.
100% gold efficiency means the item is granting as many stat points as if you had spent the same gold on the raw stat items; A higher gold efficiency means you're getting more stat points.
As for the stacking portion of your question, its best handled in a separate question. The short version: If you own the item, you can have double auras, no more; everybody else gets a single aura.
Gold Equivalencies
- Rejuvenation Bead (180g) = 5 health regen; 180/5 =
36 gold per 1 health regen
- Cloth Armor (300g) = 15 armor; 300/15 =
20 gold per 1 armor
- Null-Magic Mantle (400g) = 20 magic resistance; 400/20 =
20 gold per 1 magic resistance
- Ruby Crystal (475g) = 180 health; 475/180 =
2.63889 gold per 1 health
Item
250 health, 20 armor, 20 magic resistance
250 * 2.63889 + 20 * 20 + 20 * 20 = 660 + 400 + 400 = 1460g worth of stats
Aura
10 armor, 15 magic resistance, 10 health regen
10*20 + 15*20 + 10*36 = 200 + 300 + 360 = 860g worth of stats
Now, if the aura hits 1-5 champions:
1460g + 860g * 1 = 2320g worth of stats for 1 champion, 107.32% efficient
1460g + 860g * 2 = 3180g worth of stats for 2 champions, 147.91% efficient
1460g + 860g * 3 = 4040g worth of stats for 3 champions, 187.91% efficient
1460g + 860g * 4 = 4900g worth of stats for 4 champions, 227.91% efficient
1460g + 860g * 5 = 5760g worth of stats for 5 champions, 267.91% efficient
The item's total cost is 2150g, so the item is gold efficient for just the item owner.
Item
300 health, 20 armor, 20 magic resistance
300 * 2.63889 + 20 * 20 + 30 * 20 = 792 + 400 + 600 = 1792g worth of stats
Aura
10 armor, 25 magic resistance, 10 health regen
10*20 + 25*20 + 10*36 = 200 + 500 + 360 = 1060g worth of stats
Now, if the aura hits 1-5 champions:
1460g + 860g * 1 = 2852g worth of stats for 1 champion, 96.56% efficient
1460g + 860g * 2 = 3912g worth of stats for 2 champions, 133.73% efficient
1460g + 860g * 3 = 4972g worth of stats for 3 champions, 170.90% efficient
1460g + 860g * 4 = 6032g worth of stats for 4 champions, 208.06% efficient
1460g + 860g * 5 = 7092g worth of stats for 5 champions, 245.23% efficient
The item's total cost is 2950g, so the item is 96.56% gold efficient for just the item owner, and is fully gold efficient if the aura is on at least one ally champion.
Best Answer
Most ap champs can use Zhonya.
The ones that make the most use of it are the ones like Swain that have an ability that keeps going even when using it.
Swain, Morgana, Kennen, Fiddlestick (ults) and Karthus (defile) are the ones, of the top of my head, that have such abilities that will keep going while under Zhonya protection.
It can also be used on squeesh ap champs that use it for the protection only and that they need to be in the middle of the fight to deal the most damage, like Fizz and Katarina. It's a life saver. It may be used on Kassadin but with his escape ability, it usually not as useful. It will be seldomly used on Annie, Brand and the other ap champs that usually are not in the middle of the fight in case they get there and needs time for another cycle of spells.
Other ap champs can still use it but some don't generally use it, like Diana and Orianna. You won't see many people running Zhonya on those 2.