I just got GOTY and looked forward to reacquinting myself with it. However, when I boot it up, while full-screen, the game runs only in a narrow area to the middle of the screen, and to the sides if it it's just black.

I run windows 7 on an acer aspire with GeForce 540 series, if that helps. How do I get it to fill out the entire screen?

It sounds like you have a widescreen monitor. Running old games that weren't made for widescreen end up leaving black bars on the sides.

To play Unreal Tournament in widescreen, follow the directions from the Widescreen Gaming Forum, which I'll post here:
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Go to <gameDir>\system. Open unrealtournament.ini. Find these lines:

FullscreenViewportX=xxxx
FullscreenViewportY=xxx

Change them to set your resolution.

Now open user.ini. Find these lines:

DesiredFOV=90.000000
DefaultFOV=90.000000

Change the values to set your FOV to your preference. I recommend 100 for 16:10 resolutions and 107 for 16:9 resolutions.
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It's most likely that if you're running on a PC (not a laptop) and you have a separate monitor, then your resolution is 1920x1080.

If this doesn't work then delete your ini file.