Unless you mean after the third partition of Poland, then maybe, but at no point in time would I ever consider Prussia's domains to be vast (at least not by Roman, Russian, Aksumite, or British Imperial standards).
By "vast," I mean, of course, that a good chunk of Prussia's territory is not located within modern Germany. Let's not bring semantics into this, though - That only gets us further away from the main point.
I would consider territory an issue because the OP seems to imply that the predecessor state has to expand into territory that eventually becomes integral to the successor state, as England did with Wales and Scotland to become GB, Castile did with Aragon to become Spain, and Prussia did with the German states after Vienna (which, as far as I can tell, is when their nationalist ambitions began). Aksum decidedly did not do this.
As I said before, however, I see Aksum, the Zagwe dynasty, and the Solomonic dynasty as three continuations of the same state. Aksum did expand into territory that became integral to the sucessor state - All of its territory
did become part of the Ethiopian Empire.
That Aksum had territory in modern Eritrea
is irrelevant - Solomonic Ethiopia did, too, just as Prussia and the German Empire had territory in modern Poland.
Yes but KoR has already established that the Byzantines are not what he's looking for, and as far as power bases go there have been many states with power bases in the same places as other ones without actually being a successor. I'm not sure either of the points you're using would help to establish your argument.
There is in the case of the Zagwe to the Solominic dynasties, but there was a long, LONG dark ages between Aksum and the Zagwe. I think it would be more reasonable to say that Aksum created the idea of a necessary Aksumitas, or a yeAksum Mengist, and credit Shewa with the rise of modern Ethiopia, since Ethiopia was about as united as the HRE before Tewodros and didn't cover most of its current territory until Menelik.
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When the Zagwe dynasty emerged, there was still a remnant of Aksum in the region. It had largely been reduced in territory, but there was still a polity in existence and the sovereignty of this polity was transferred to the Zagwe dynasty without interruption. It is this polity that I argue is the predecessor to Ethiopia. This is different from the comparison of two states that existed in the same territory without any continuity between them, like Rome and Italy, the Incas and Peru, or Monomotapa and modern Zimbabwe.
The idea of a polity growing and then shrinking again before it reaches its modern manifestation is also part of Germany's history - In between modern Germany and earlier Reichs, there is the "remnant" of West Germany that filled in the gap for some time.
I will concede, however, that maybe my view of things is looking at a bigger, broader picture than the OP is specifying - Where the OP separates Wessex as the unifier of England and then England as the unifier of the United Kingdom, I see a straight line from Wessex to England to Great Britain to the United Kingdom. That's also where I get the idea of the ancient city-kingdom of Rome as the ultimate predecessor of the Byzantines from.