I have my TV set up as the second monitor just for showing iTunes Visulisations when I'm doing other stuff on the Mac.
I couldn't get iTunes to do what I wanted (fullscreen on second display), so I wrote a little Applscript
tell application "iTunes"
activate
set visuals enabled to true
set position of window 1 to {100, 100}
set bounds of window 1 to {0, 0, 1065, 900}
set position of window 1 to {1900, 118}
play
end tell
I added the script to the library/iTunes/scripts folder and now when I start iTunes I can run the script which resizes the iTunes window and moves it so that it completely fills my second screen (the TV).
The window does still have the surround border, and it does overlap my primary screen a bit, but I'm happy enough.
You might have to play with the position and bounds figures to get a good position for a different screen.
Wow, my first post - hope it's some help.