Arnorian successor states? 3 or more

[Belegorn]

After Eärendur passed away Arnor broke into 3 kingdoms held by his sons. The eldest held sway in Arthedain and this line continued whereas the line of Amlaith's brothers perished.

Originally Posted by Appendix A: The North-kingdom and the Dúnedain

the line soon perished in Cardolan and Rhudaur.

By the time of Argeleb [1226-1356 T.A.] there were no other descendants of Isildur in the other two kingdoms. It was due to this that they started reclaiming lordship of Arnor and this accounts for the Ar- prefix in their names since then.

Originally Posted by Appendix A: The North-kingdom and the Dúnedain

the kings of Arthedain again claimed the lordship of all Arnor... since no descendants of Isildur remained in the other kingdoms

There were still Dúnedain in those other kingdoms even when the other descendants of Isildur perished. They did perish in Cardolan in 1636 after the Great Plague hit them.

To your question, it would seem there were no other lesser kingdoms. When lesser kingdoms is mentioned in the text I think it refers to the 3 lesser kingdoms that formed after Arnor broke apart, "The sons of the king established smaller independent kingdoms." [Heirs of Elendil; The Northern line of Arnor: the Isildurioni] They were lesser kingdoms all than Arnor. Chief of those lesser kingdoms [Arthedain, Cardolan, and Rhudaur] were "Cardolan south of the Great Road and east of the Baranduin; and Rhudaur north of the Great Road between the Weather Hills and the Bruinen."

[IxnaY AintsaY]

Here's a bit more of the text to which Dúgorin is referring to, I think. On my copy, it's on page 193, within "The Northern Line of Arnor: the Isildurioni [!], and underneath the entry for the 10th King of Arnor, Earendur (The bracketed material is in the presented text, representing a strike-through that Tolkien made himself.):

After Earendur the Northern Kingdom of Arnor was broken up. The sons of the king established smaller independent kingdoms. The direct line of the eldest son ruled the realm of Arthedain in the North-west; their city was Fornost. Annuminas became deserted owing to the dwindling of the people. The chief of the lesser realms were [Cardolan east of the Baranduin; and Rhudaur north of the Bruinen. Arthedain still claimed the overlordship, but this was disputed. >] Cardolan south of the Great Road and east of the Baranduin; and Rhudaur north of the Great Road between the Weather Hills and the Bruinen.

I agree the wording doesn't make sense given that there's no other hint of successor-states to Arnor besides Arthedain, Cardolan, and Rhudaur. But more to the point, Arthedain is everywhere else presented, if not as the chief of the three, than certainly not the underling of Cardolan and Rhudaur!

Personally, given that the writing is a little disjointed anyway, I'd guess it's either a mistake by JRRT, or a corruption in the text we've been given by CT, or by his editors. Or possibly it was a passing thought by Tolkien that was dismissed or forgotten. But I'd lay a nickel on it being a mistake.

* * *

As an aside, I can't help but be reminded of Tolkien's line in Unfinished Tales, "The Istari":

"Of this Order, the number is unknown, but of those that came to the North of Middle-Earth, where there was most hope (because of the remnant of the Dúnedain and of the Eldar who abode there), the chiefs were five."

[Belegorn]

Good point about the Istari Ixnay. I think that the kingdoms of the two younger brothers [of Cardolan, and Rhudaur] are pointed out as the greater of the lesser realms [those being Arthedain, Cardolan, and Rhudaur] as Gondor [line of Anárion] was greater than Arnor even though Arnor [line of Isildur] was the state of the elder line. Arthedain [line of Amlaith] was the kingdom of the elder line as well, but the younger lines appeared to have the greater power, though probably not so great as Gondor to Arnor.

It is clear that aside from the House of the Kings, there were other princes [like in Gondor]. After the line of Kings died out in the kingdoms of the younger brothers, in Cordolan there was still a prince until 1409 which is at least 53 years after the last kings there perished.

Take a look at the map and the borders of the three kingdoms in Eriador. Could some smaller realm exist there where Arnor used to be along with those 3 kingdoms? Would they have branched out into territory previously not held by the lords of Arnor?

[Kuruharan]

Originally Posted by Belegorn

Good point about the Istari Ixnay. I think that the kingdoms of the two younger brothers [of Cardolan, and Rhudaur] are pointed out as the greater of the lesser realms [those being Arthedain, Cardolan, and Rhudaur] as Gondor [line of Anárion] was greater than Arnor even though Arnor [line of Isildur] was the state of the elder line. Arthedain [line of Amlaith] was the kingdom of the elder line as well, but the younger lines appeared to have the greater power, though probably not so great as Gondor to Arnor.

That is an interesting take on it because I had always been under the impression that Cardolan and Rhudaur were weaker than Arthedain.

[Inziladun]

Originally Posted by Kuruharan

That is an interesting take on it because I had always been under the impression that Cardolan and Rhudaur were weaker than Arthedain.

That supposition would seem to be borne out by the fact that they ended before Arthedain.

[IxnaY AintsaY]

Originally Posted by Inziladun

That supposition would seem to be borne out by the fact that they ended before Arthedain.

Maybe. I certainly feel Arthedain was at least stronger than Rhudaur, and -at least- equal to Cardolan, but I haven't been able yet to find a definitive textual support for that feeling. There is though this later note in "The Heirs of Elendil" from two versions of a page in an earlier manuscript than the one I excerpted (Page 209, under "Argeleb I" a king of Arthedain.):

'Slain in battle 1356. Angmar is repulsed but turns upon the lesser kingdoms.' [The replacement page has:] 'Slain in battle with subkingdoms of Cardolan and Rhudaur'.

Bracketed insertion is CT.

[Belegorn]

In Of the Rings of Power and the Thrid Age it is said of Arnor after the passing of Elendil that "of the Númenóreans and of the Men of Eriador there remained now too few to people the land or to maintain all the places that Elendil had built". This may be useful for your question of the possibility of more than three kingdoms. The kingdoms were taken out one by one, as they diminished due to infighting and of course war with Angmar. I do not know if Arthedain was the greatest of these three realms, but its royal line was maintained where it faded away in the other two, as well as the line of princes in the other kingdoms. The other two kingdoms did fade in their strength faster than Arthedain which is why it was pointed out that Argeleb l was slain in battle with the subkingdoms. During his time the royal line was not existent in the other two kingdoms anymore and perhaps those two kingdoms did take a hit with their passing.

[Kuruharan]

Originally Posted by IxnaY AintsaY

'Slain in battle with subkingdoms of Cardolan and Rhudaur'.

I think the telling comment is their reference as "subkingdoms."