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I can't say it varies.
One site I moved took googlebot around 3 weeks to find the new DNS.
I moved one site around 3 months ago (dns fully propagated) and STILL googlebot goes to the old server.
I am not going to pay for 2 hosts just to keep google happy, so I am waiting for the next update and then I will be taking the old site down.
I have emailed them but never a reply and still googlebot goes to the old site.
Dazz
P.S. In defense of Googlebot, they do spider more pages more often than all the other search engines combined, in my opinion. To do that, they have to move fast.