Salvete,
Lucius Tyrrhenus Garrulus wrote:SALVETE OMNES, S.V.B.E.V.
When the last emperor called it quits, did Rome still possess any geo-political/military authority? If so to what extent, and for how long? Were there Romans who didn't know the Empire was no more?
MVLTAS GRATIAS ET VALETE BENE!
Roman military authority was nearly non-existent near the end. Rome had already been sacked by the Visigoths in 410 and again by the Vandals in 455 and it never recovered from that blow. I presume the idea that thé Urbs Roma could be simply invaded and sacked must've proved almost as great a shock to the barbarians at the borders as it did to the Romans themselves.
What Rome did continue to possess was great
symbolic political authority*. Thus, when Odoacer deposed Romulus Augustulus in 476, he went to ask the East-Roman Emperor Zeno to recognize him as consul under his authority. Zeno granted this, and thus - theoretically at least - became the first emperor of a united Roman Empire since Theodosius in 395. This situation would not last for long however, as Odoacer soon began to violate the terms of their agreement. Still, I find it rather remarkable that Odoacer chose to submit to the East-Roman authority instead of simply ruling in his own name, which he could easily have chosen to do. Also, he largely retained the Roman administration as it had been in late antiquity. Apparently, people were not yet able to think of any form of government that could replace Rome's system.
Valete,
Atticus
*In fact it continued to do so in a way for millennia, from Carolus Magnus to Mussolini so to say.
N.B. : I'm writing this from memory, so if any mistakes slipped in, feel free to correct me.