So you use your TV as secondary display on your Mac, and Elgato's EyeTV to watch "live" TV? In that case, the recently introduced Full Sceen Menu mode of EyeTV will be pretty useless for you -- it always appears on the primary display (as does the picture-in-picture box). There is no option in EyeTV's preferences pane to change this behaviour. After some searching, I found the solution on their FAQ pages. Go to the Terminal and type the following line:
defaults write com.elgato.eyetv
"preferred fullscreen device index" -int 1
To change back to the standard behaviour (Full Screen Menu on primary display), use the value -1 instead of 1:
defaults write com.elgato.eyetv
"preferred fullscreen device index" -int -1
This worked just fine for me! You can read the full writeup on ElGato's FAQ page if you need more detail.
Mac OS X Hints
http://hints.macworld.com/article.php?story=20061130002604839