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When I'm using regular league I can be playing on my secondary monitor while it switches from air client to the game and 99% of the time fits my main monitor just dandy.
Spectator mode on the other hand has an issue where it will keep your main monitor's resolution and shift down and to the right (secondary monitor on the right) so it's about 50% from the top and left of my main monitor. It's very annoying and if I change video mode from in the game down to 1024x768 then back to 1920x1200 it moves back to proper position.
If I need to I can post a screen shot but it's pretty annoying. I do know that the main client used to do this also but I'd say about 4-6 months ago was fixed.