In Geoff Pullum's recent post Being an Auxiliary on the Lingua Franca blog, he states that the sense of "have" as an auxiliary (forming the perfect tense) evolved from the possession sense, "but the speciation that separated them took place half a millennium ago".
This struck me as much too recent, given that an almost identical perfect construction exists not only in most (all?) other Germanic languages, but also in the Romance languages (with the exception of Portuguese?). But, sure enough, the OED says that this evolution "to some extent parallels developments in other Germanic and Romance languages, but appears at least partly to reflect development within English". (On the other hand, it also says "This development appears to have largely taken place before the written record.")
Assuming that it indeed happened within the last half millennium or so, how can this kind of fundamental language change occur in parallel between a dozen or so languages dispersed over a continent (from Iceland to Romania)? Did the innovation occur in one region and then spread between languages (like a new vocabulary item might), or is it better to think of it as a natural development that came about independently in multiple language communities (like simplification of noun inflection)?