Sort of. I found that I had three computers authorised, but I could not remember what they were. I was comfortable that the one I was using (the one I'm using now, our main family PC) was authorised, but I could not tell, or recall, what the other two were. I ended up just de-authorising all computers and then re-authorising this one. But at no time did iTunes provide me any detail of the computers. Seems to be a very strange and opaque process to just deal with nothing but a raw number, rather than specific details of each computer. Strange too that details are provided on "associated devices" but not "authorised computers". Am I missing something or is that just the way it is?