First, I apologize if this is a question for a linguist. But how long after the Fall of Rome (or even during) did they come about? And did they come about because of regional dialects of Roman Latin?
This is a question for a linguist, but any answer you get will boil down to "gradually" as a result of the breakdown of the imperial infrastructure during the "Dark Ages" -- a pejoratively named yet chaotic time of which few written records remain. They do result, for the most part, from regional dialects of Roman Latin.