I always found myself scratching my head thinking "that's all they had to do? Blow up the Death Star while the Emperor and Vader were on it"? We're talking about an Empire that spanned how many star systems? There's no chain of command beyond the Emperor and Vader? Of course the old EU covered this to some degree, and some folks thought it was redundant, "fighting the Empire AGAIN?", but it actually makes sense. The Old Republic didn't fall because it was defeated, it fell because it was gradually transformed into the Empire.
Seems like in the new canon, the Alliance just rested on its laurels and hoped everyone would fall in line and follow the New Republic, while in reality, normal folks on most planets probably didn't care enough, and were still under Imperial control. They drew down their military force and didn't seem to go for the "retake the galaxy star by star" from the Empire doctrine.
Yes, there must have been a lot of Imperial ships and personnel still active after the battle of Endor; this might explain all of those TIE fighters we see in VII. That said; what happened to all the clones? Fin certainly wasn't one.
I used to see the destruction of the second Death Star, and the deaths of the emperor and Vader as being similar to the way in which the Kilrathi fell apart after the destruction of Kilrah. Now it's explicitly stated in the rules at the CIC not to make comparisons between different universes, but this is more for the purpose of analogy. After Kilrah fell, the Kilrathi immediately surrendered (as Taggart suggested they would) - followed by Kilrathi clans fighting and scrambling for power. I always thought that the destruction of the Death Star would have been a similarly demoralizing blow for the Imperial forces, combined with planets gaining confidence and overthrowing their Imperial overlords (in the re-mastered ROTJ we see a statue being pulled down and feverish celebrations on many worlds).
Maybe though, what actually happened - as you suggested, was that many of these worlds remained under the control of the remnants of the Empire. Since we hear about the 'Republic' in
The Force Awakens - perhaps we can deduce that the Empire became more of a 'faction' than a ruling power. It became the First Order.
Also note, I haven't read any Star Wars extended universe or novelizations (man, it pains me to spell that word with a 'z' - but the CIC forum is a largely American audience
...when in Rome...)
