About Mavericks
One of the best things Apple has done with OSX Mavericks is the feature of keeping the extended desktop (external monitor) separate. In the sense that, unlike before, it's somewhat disconnected from the main desktop. This means that it's now possible to have maximised applications on each of the desktops -- and thus fixing the limitation in the previous versions of OSX where an app could be maximised on either of the screen. It beats me on how did that feature seep-in in the first place.
Anyway, so again, unlike before, AppleTV now allows you to use the connected monitor as a secondary desktop as well. Finally, someone seems to have put brains into these pesky little flaws.