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I belive that you need to adress this question to the nearest questura.

I specifically remember my sister asking/doing the same thing after her permesso expired from studying in Florence. You are legally suppose to leave once your visa/permesso are expired.
However, I have lived in and off in Italy for 4 years (while waiting to have my perm permesso accepted and validated) and I never once had an issue coming or going. (Just for reference I'm American - and while this shouldn't make a difference...)

Hey guy, well I asked at the questura, and to be honest they told me a lot of bs.  They said I had to go back to Australia when my study visa expired, and then I wasn't allowed to re-enter Italy for 6 months as a tourist!!   This makes zero sense and is a rule I had never heard of before.  So I did some more research, and I am reasonably confident that I would be allowed to stay as a tourist, provided I left the Schengen zone BEFORE the expiration of my study visa, and then re-entered afterwards (and got a stamp when exiting/re-entering).  This is because the Schengen Border Code states that time spent in the country on a long stay visa (such as a study visa) does not count towards the 90/180 rule for tourist visas. 

Not sure if I can post links, but here are some other forums where it is discussed:

travel.stackexchange.com/questions/36541/help-with-student-visa-and-tourist-visa.   

.maxi-pedia.com/forum/index.php?topic=288.0

lonelyplanet.com/thorntree/forums/europe-western-europe/topics/can-i-travel-europe-after-my-long-stay-visa-expires

.fodors.com/community/europe/schengen-visa-question-student-visa-visitor-visa.cfm

Hey! How did you work it out then?

-)

I stayed on 3 months past my study visa without problems. I was in London for 3 days when my visa was due to expire and got the stamps (just in case). I left Italy several times (even did a trip to Australia) and there were zero issues.