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How long before this is transferred to the Google directory? As far as I can tell from searching, there are only links to .net from Google directory and a few "DMOZ copy" directories, which I don't expect to change so fast, and are of little or no importance.
Once it's changed on Google, we can kill the .net domain once and for all. I could do a redirect...except I don't have a clue how. Our site is done by ourselves and we are not pro webmasters.
Your site change will be in the first file created after the change was made.
Now as to when it will be picked up by Google and the other directories using ODP data is unknown. All downstream users of the file can take it anytime - Google used to be on a 4-5 week schedule, but some directories have not updated in several *years*.
If you are, instead, referring to the Google *search* indexing the change - that is done duringthe normal google 'monthly' cycle. It crawls DMOZ, just like it crawls all other sites it finds links to. This is independent of the Google Directory.
After all that - no one knows! You'll just have to wait for it to happen. :)