An odd scenario with 2 G4's & LW Playlist within iTunes

[Lord of the Rings]

I have an odd situation. 2 mac G4's ("A" & "B") which are not networked but do share the same router. One of them ("B") has never had LW program on it but for some reason the iTunes on comp "B" has the LW Playlist (Let's call this Lotr's Limewire music.) Perhaps a dozen songs have been downlded via LW on comp "A". These were copied across to the other comp ("B") either via zip disk or cd-rw. There is an external HDD which "A" uses only as a backup of music, video & photos. It has only been connected to comp "B" a handle of times ... once for repair via Norton. But no music was copied from "A" to "B" this way (& it hasn't been connected to it since long before the songs were copied across.) There is also an iPod that is manually loaded via comp "B", but this iPod has never been connected to comp "A".

Now here's the confusing part, the LW Playlist which shows up in the iTunes playlist on comp "B" can be played by iTunes. But the songs don't exist on the computer!!! Searches don't find any of the songs on there. How can this be!

The questions are obvious ... how did the Lotr's Limewire music playlist get onto comp "B", & how can it be playable when the songs don't exist on the computer?

If anybody can solve this mystery I'd be much obliged. (We're bamboozled (confused) here!)