To get this back on topic somewhat, perhaps a history refresher course is in order, if I may be so condescending. Of course I may, it's me. Let's just cover the Molossian thing first... The word stands for mountain-sized greatness of a mountain dweller, be it hunting, fighting or knitting sweaters, whatever - it's rustically grand. Molossians were people and molossian dogs were their pooches. Molosser should trigger thought of "mountain" immediately, that's why I nitpicked about the FCI definitions and common usage deviations, equating giant Pugs with "molossian" dogs etc. The reason why I've gotten the reputation as a pusher of mountain mastiff malarkey is because that's what a molossos is - a hillbilly giant. Man or beast. The dogs under the name were mountain dogs of the mountain people. I wasn't pushing LGDs, I was pushing [u]molossers[/u]. Here's the skinny:
Molossus was Achilles' grandson, right? So this Molossus fella steals Cerberus, the big black 3-headed helldragon, see? He was hiding the dog in a cave so Hercules wouldn't find him, as it was Hercules who had kidnapped the dog from Hades initially for some very important reason, surely. Anymyth, our boy Molossus manages to get a litter out of Cerberus and a sheepdog bitch, using the puppies as the foundation for the original Molossus' dog. So, a dude named Molossus had a dog.
Molossia? Founded by descendants of our friend Molossus, the original stud-stealing bandogger. Molossia existed and now it doesn't. Hasn't been a thing in quite some time. There's something it has been at any point in history. A mountainous area full of roughnecks and big scary dogs. They had something special in 'em and that's all there is to it, really. Whether it was Cerberus blood or some Sylvan fantasy or whatever isn't even important. They had dogs which were desired by others, simple as that. People are too stuck on the "they" part, since everyone would like to be descended from something whose contribution to history can be claimed ownership over, but the "they" is whoever lived in the region and not any silly "relevant" nation. The only reliable "they" in the story are the Romans and THEY sure as sh*t wanted them some Molossian dogs.
And it's not like Molossians were the only ones with good dogs during their glory days. What we call "ancient Greece" was chock full of all kinds of "breeds" and tribes of "dogmen", many of which left better documentation in their wake than any pre-Roman molosser thing. All of those other families could've potentially been even more interesting to research in comparison, but then again, perhaps their "branding" wasn't strong enough. If it made such a lasting impression on the Romans, the molossian thing must've been the bomb.
What else? Oh yeah, this can never be repeated enough - Alexander didn't own any Molossian dogs. He dug the hounds from the east. The famous one, Pertio or something (I'm getting old), was a little Indian dog, never recorded as anything else. Apart from his mommy supposedly being descended from that same Cerberus-stealing dude, the Great's got zilch to do with Molossians, btw. Most of the nonsense of animal baiting dogs in his keep skips over the part about Alexander's rule being one which instituted animal protection laws and punished abusers of dogs. Everywhere he went. He never received any "albanian" dogs he used for killing elephants, either. Most of what's nowadays parroted about old Al was concocted in the last 3 centuries. Same goes for the Molosser.
The point is, Romans could've called them anything, but they specifically maintained their Molossian name. Not because they were some furry hound that existed just anywhere, but because they were from Molossia where their reputation had already been established and investigated by the Romans. So yes, the Romans brought a big gripping sheepdog from the mountains in southern Balkans to the "Boot" and perpetuated those Molossian genetics for much longer than the original Molossians existed on this planet. The Molossian dog was the foundation for the "molossoid" family, if you will, but other types of dogs were even more influential in those subsequent genetics.
P.S. Molossoid as a term has done more damage than good as it leads folks to confuse a geographical notion with a convoluted biological definition. And a great majority of "molossoid breeds" got nothing to do with Molossia or Molossian dogs. Unless it is to strictly distinguish mountain dogs and shepherd's mastiffs "in honour" of the Molossian dogs, it's a flustercluck of a barrier in learning.