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Now, backlinks and related traffic . . . that's a different matter. However, depending on what you do to take advantage of those old links to your new site, you could get yourself in a bit of trouble.
Also, if you are thinking in backlinks=traffic mode, if you don't already know so be advised that there will be lots of competition - very smart competition - for the specific domains. (That's not to say that you're not as smart. ;) It's more to say that the people playing this game have a great deal of data that they work with, that informs their purchase decisions.)