I've just updated to Mavericks, and while I like having the dock on my 2 Landscape displays, my third portrait display is entirely unsuited to having a dock on it.
How can I suppress the dock from appearing on one of my 3 displays?
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I can't find any way to allow the dock on 2 of the 3 displays.
But, there are some things you might do.
In Mavericks, the default is that each monitor has its own Space, an Apple way of saying that each monitor is its own independent desktop.
The implications of that are that your menu bar will be on all monitors but "disabled" on the monitors that you are not currently focused in. It also means that the dock will automatically change to the monitor that you are focused in.
You can change this setting so that the monitors are one Space, or one desktop. In "System Preferences" > "Mission Control", deselect the box for "Displays have separate Spaces".
Now, your menu bar and dock will only appear on one screen and will not move automatically.
To change which monitor is your primary monitor, go to "System Preferences" > "Displays". On the monitor that is your current primary monitor, a tab on the top of the window will say "Arrangement". There will see the side-by-side layout of all the monitors. Click and drag the white box on the top of your primary monitor to a different monitor to change which is your primary.
The new primary will have your menu bar and dock.
Note: This assumes you have "Displays have separate Spaces" turned on.
The Dock only appears on one display at a time. To move it between displays, simply hold your mouse pointer at the bottom of the screen you want until the dock appears.
(The screen with the Dock on it will also be the one with the ⌘⇥ app switcher.)