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Hope it goes as smoothly for you ... don't think it'll be a problem if your provider does everything 'right'.
Google found the new site within a few days of the move, and most of the traffic has been diverted to the new server.
I do check the logs of the old server (the site is still there) and noticed that it gets a few visits per day by several spiders. I will leave the old site up for another month just to accommodate these spiders.