How to broadcast desktop to TV from multiple PCs?

Question

VNC

In general, the situation: A
spherical office in a vacuum, 3-5 workplaces, a TV set on the wall.
Wishlist:
Each workplace has a magic button "transfer image to TV", when you press it on the TV, the video captured from the screen of this workplace starts.
If on another slave. place the "magic button" is pressed, but the broadcast switches to it
Tell me which way to dig ... I'm thinking of doing it through vnc, but how to make the client listen to several servers, and work with the one that last connected ....
or maybe even anyone have any helpful thoughts on this topic