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First, it's important to understand the terminology. A display is a physical monitor, typically a flat panel LCD device. This article focuses on a second external monitor connected to, say, an iMac or MacBook. An OS X desktop resides on a display and has a menu bar at the top and (generally) a dock at the bottom. An OS X Space is a extension of the desktop that has a menu bar and dock where apps may reside — either duplicated or in isolation.
Multiple Spaces assigned to a desktop.
Mavericks has two operating modes, defined in System Preferences > Mission Control. The option “Displays have separate Spaces” determines whether your two displays act as separate desktops, each with its own menu bar and unique Spaces (checked) or, alternatively, both displays are one desktop with only one menu bar (unchecked).
A log out is required after you select this option.
In the first case, (checked) the display that has the active menu determines which independent Spaces you step through when you toggle with CTRL + Right/Left arrow. Each desktop has its own Spaces, and each space can have its own wallpaper.
In the second case (unchecked), you have one desktop with one menu bar and (optionally) multiple Spaces. The Spaces stay in sync on the displays as you step through them with CTRL + Right/Left arrow. However, each can have its own wallpaper. In other words, two displays comprise one desktop. The desktop can have N number of Spaces that span both displays.
This tip refers to mode #1 (checked.)
Assignment of Apps
Let's say that in mode #1, you'd like to assign a given app to specific desktop. The way you'd normally do that is to right-click the app's icon in the dock. However, and here's the gotcha, if you only have one Space assigned to that desktop, the dock option (to make an assignment) does not appear.
With no extra Spaces defined.
The trick is to assign a second Space to the desktop. You do that by pressing the Mission Control button on your Mac keyboard (F3) or whatever you've assigned in System Preferences > Mission Control, and moving the mouse to the upper right of the display until you see a Plus (+) icon. Click it to create a new Space.
After you've created a second Space, your dock option will change. Now you'll see this:
AFter a second space has been defined.
Now you can assign the app to the Desktop of your choice, typically either the desktop on display #1 or display #2.
Why you have to create a second Space for that desktop before you can assign an app to the desktop is not understood by the authors at this time.
Moreover, the behavior of the “Assign to” function appears to change across apps. For example, if you were to assign an app to desktop #1, and then move it to desktop #2 right before a log out, it may honor the assignment on log in or it may stay where you put it.
The assumption here is that the election has been made to have the app relaunch when logged back in. Otherwise, it has to be relaunched manually (unless you've designated it as a launch item in System Prefererences > Users & Groups > Login Items).
Option to relaunch curent apps & windows at log in.
We have discovered that some apps honor the assignment made in the dock no matter what after a log out/log in sequence or a restart and some stay where you put them. Experimentation is recommended. This tip is really focused on getting to the assignment mode in the dock in the first place.
Apple's implementation could have been cleaner, but the authors suspect that various apps have not been recoded to honor the Mavericks way of doing things.
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MacBook Air teaser image via Apple.