I do not have any files associated with Limewire on my Ipod. The "sharing Limewire" is on the left side of my Itunes window.

When you connect an Ipod to your PC with Itunes running, an icon shows up depicting that the Ipod is connected and available.

When you put a music CD in the drive while Itunes in running, an icon shows up showing that the CD is available to be used by Itunes.

SO NOW, ALL OF A SUDDEN, I have a new icon depicting that Limewire is available.

I DID NOT DOWNLOAD IT NOR DID ANYONE ELSE. I DO NOT HAVE A MENU FOR LIMEWIRE, it only appears in Itunes. I can ONLY CONNECT OR DISCONNECT nothing else.

COULD THIS BE THE PROBLEM: I was just told by someone that if I have a wireless router in my home and all of our computers are logged in to the wireless router to connect to the internet AND IF ONE OF THOSE COMPUTERS has Limewire loaded, the "sharing" icon will show up in Itunes in ALL COMPUTERS attached to the same wireless router. Is that possible?

Stop SHOUTING

If you'd done a simple forum search, you would've found out that the 'shared LW tunes' playlist that you see in iTunes only shows if iTunes sharing is enabled within LW's options. If you didn't download LW then either someone else used your computer to download LW or you're on a LAN, connected to someone who has iTunes sharing enabled in their LW.

Tell whoever has LW installed to turn off iTunes sharing (tools > options > sharing > iTunes. Untick 'share my music' > Apply > ok) & you won't see that playlist any more.