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This process may take a few minutes to an hour or so, depending on your internet connection.
Alternatively, you can copy over emails it a step at a time -- which is particularly useful on slower Internet connections. Simply highlight say a month of emails and move them over in chunks. Repeat until all emails have been moved over.
To read more on this gallery, visit the iGeneration column, where you can read more about migrating your email to Hotmail or Gmail.