What is the best way to move purchased music from my G4 laptop to my desk top Mac so I can de-authorize the laptop and sell it.

Do you have a music library already on the desktop you want to preserve? If not, you could just copy the entire iTunes library to the desktop.

If you are trying to add this music to an existing library that you do want to keep, you could connect to the laptop over your network, and then use Command-O to select those tracks and add them to your library. It does mean hunting them all down, though.

Another way would be to burn the purchased tracks to CD/DVD. There is a back up feature (I haven't used it) that you might want to try. Go to File->Back up to Disc (I haven't used this myself).

Easiest way would be to use a FireWire cable and put the G4 notebook in "Target Disk mode" and just copy the files from the old unit into iTunes on your new iMac. Did you migrate data using Migration Assistant? That would have moved your music already.

Used Jack's approach since it was a small library. I burned it to CDs and then on my G5 I launched iTunes and it asked me if I wanted to "Restore from disc" > then I had to select whether or not to erase the current library. Worked slick- even put the movies and TV shows in the right places. Thanks Mr. B.