The full extent of the Reunited Kingdom
 

So we have a glimpse of middle earth's future as it marched into the fourth age. I am curious though how big did the Reunited Kingdom get. Aragorn and Eomer pursued campaigns around the sea of Rhun and subdued Harad(or the northern parts at least). But could Aragorn or his descendants have subdued all of Middle Earth all the way to the eastern sea and the Dark Land? Or would it remain beyond their grasp.

Also based on that question how did the reunited kingdom end? We know Tolkien considered Arda to be an ancient Earth so Aragorn's empire must have ended at some point or another.

Anyone want to hazard to answer these questions. They are speculative of course but speculative answers are what I am looking for.

Unfortunately, the only answer that can be given is, "We don't know." Aragorn's conquests was a topic that Tolkien only touched upon in the vaguest of terms.

That being said, I find it implausible that Aragorn or his successors could have subdued the whole of Middle earth. The Reunited Kingdom was already a vast territory of nearly ungovernable scope, and initially, very thinly populated to boot. I don't think that any additional conquests could have been large or sustainable.

As for how it fell, Tolkien did write some pages of The New Shadow where in the time of Aragorn's successor Gondor was already starting to unravel. I don't know that we should suppose that the Reunited Kingdom's dominion was of any great duration.

It certainly wouldn't be unprecedented historically for a great empire to be expanding its borders while at the same time rotting at the core - and the same went for Numenor. From Tolkien's viewpoint the two would probably be linked, since conquest for its own sake was in his view a mark of degenerate kingship.

Why would Gondor have been rotten morally or otherwise?

In The New Shadow, as Kuru notes, people in Minas Tirith were basically forgetting what it was like to have lived with the fear of Mordor. Boys were running around being vandals, pretending they were Orcs. And this was in the reign of Eldarion, Aragorn's son. Like Men of any level of nobility or virtue, they soon grew tired of peace and stability. As high as the Númenórean remnant of Gondor were, as time went on they would inevitably become more like other Men of Middle-earth, with their history as Edain receding into dim memory.

I think it might have taken quite a while for them to have developed any 'imperial' designs for their neighbors, but a greedy King coupled with a dissatisfied populace could have started things up.

The implication I take from this is that the spiritual or moral side of the kingship would wither away, and that perhaps even Eldarion may have been more an administrator than anything.

I don't think Aragorn and Éomer's campaigns in Harad and Rhûn were ones of subjugation and conquest. I think they were to subdue or force into peace those Men who refused to make peace after the fall of Sauron.
I notice a lot of fan maps seem to draw the Reunited Kingdom's borders around Near Harad and the Sea of Rhûn, but these quotes don't suggest conquest to me.

I doubt the Reunited Kingdom was ever much larger than the traditional heartlands of Gondor and Arnor, and I would think it very unlikely that its territory ever reached anywhere near the extent of Gondor alone during the reign of Hyarmendacil:
I don't get the impression Aragorn's kingdom was anything close to this. Of course I might have forgotten something. There's always an extra bit of info about the Fourth Age lurking somewhere.

I suspect the Reunited Kingdom would have gone ahead and reasserted its ancient nominal claim to everything west of the Mountains, except Rivendell and Lindon, and Rohan by ancient treaty - easy enough given a complete lack of rival claimants or meaningful opposition (the Shire, Bree-land, Orthanc, Fangorn, Druadan Forest and the Glittering Caves were "under the protection of the sceptre.") South of the Gap of Rohan, Ithilien of course; one gets a vague sense that when Aragorn "gave" Nurnen to Mordor's freed slaves it was thereby also something of a Gondorian protectorate. But I don't see Aragorn's ambitions extending farther than the Poros, unless he decided it was time to subdue Umbar once and for all. Rhun? Punitive raids against Sauronian dead-enders, yes, but there's no way Gondor could have meaningfully held all that territory.

In short, I think Elessar was concerned with re-establishing Elendil's kingdom, but no more.

An excellent opportunity to get lost in some weeds...
 

This is true, but I question whether that applies in this case due to the thin population of the Reunited Kingdom and its consequent lack of sustained military resource to expend on expanding the kingdom.

I don't think in Elessar's time, or even Eldarion's, the Dual Kingdom would have either the capacity or the intention to expand beyond what it's borders had been at the time of Sauron's return, a mere 80 years before. This would in effect mean Ithilien, from the northern end of the Ephel Duath south to the Poros, and nothing else (save reasserting a nominal claim to Minhiriath and Eriador). Certainly no point in expanding back north to the Argonath- nothing arable or even really habitable there any more. As I said, the behavior of the Corsairs might result in Umbar being retaken, but I doubt Elessar would bother with it unless provoked.

However, after 2 centuries of peace and prosperity the population might well be substantially greater; I wouldn't be at all surprised if the fall of Sauron led to something of a "baby boom" (certainly it did in the Shire!). By the mid 3200s Eldarion's son might have developed an unhealthy obsession with maps from the time of Alcarin....