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I have a MacPro, Macbook Pro, Apple TV, Iphone 2G, iPhone 3GS, Nano and 2 ipods but iTunes only acknowledges my desktop and notebook as computers.
 
I have a MacPro, Macbook Pro, Apple TV, Iphone 2G, iPhone 3GS, Nano and 2 ipods but iTunes only acknowledges my desktop and notebook as computers.

Because they are the only two computers...

What you are authorizing is the computer (i.e. the place your library is stored permanently, not on an "as synced" basis) to play/administer the content.
 
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