Manage Devices removed by mistake

Hi,

I have been rebuilding my three computers (several times) over the past months.

Today I went onto iTunes and in the Manage Devices, I 'removed' a computer (the laptop) by mistake.

(two computers were listed there that seemed to be phantoms so I removed them but finger fumbled on the above Laptop)

How can I get it back onto the Manage Devices screen?

The laptop in question is definitely 'Authorised'

I guess that I do not understand the difference between 'authorise' and 'associated' - except the iPhone only merits the latter.

Any help appreciated.

GTH