You can get the Dock to appear on any single monitor of a multiple monitor setup, but with a caveat.
Since all displays form a single virtual display surface, there is only one "Right" and one "Left" but multiple "Bottoms" if the displays are organized horizontally from left to right. If you organize them vertically there are multiple "Left" and "Right" but a single bottom. Not sure what will happen if you form some sort of "L" shaped pattern as I only have two monitors in my setup - would guess that the rule still holds but unable to verify - perhaps OP can verify with his triple monitor setup?
Unfortunately, only the horizontal Display layout and the "Bottom" Dock setting will allow the Dock to migrate to whichever screen bottom you place the cursor at (takes a second or two for the Dock to appear on the new monitor). So if you have a horizontal arrangement (which you can change in the Displays System Preferences pane) , select "Bottom" for the Dock location in the Dock System Preferences pane, and if you move the cursor to the Bottom of any of the monitors the Dock should appear there in a second or two (I verified this in a two monitor setup - so hopefully OP can verify this in a three monitor setup).
If you have a vertical arrangement, selecting either "Right" or "Left" for the Dock location in the Dock System Preferences pane, and the Dock DOES NOT MOVE to the corresponding monitor edge you move the cursor to - inconsistent and a BIG BUMMER.
This has been the case for quite a while - at least since Yosemite (I verified on a Yosemite two monitor setup also).
I learned this from the article at http://www.techradar.com/how-to/computing/apple/how-to-use-the-mac-os-x-dock-on- all-monitors-1311709
Good luck...
