Arnorian successor states? 3 or more

[Belegorn]

It seems to me in the beginning, when they had the separation, that Cardolan and Rhudaur were considered the greater of the fragmented kingdom.

Originally Posted by Heirs of Elendil; The Northern line of Arnor: the Isildurioni

The chief of the lesser realms 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.

Also keep in mind, it appears that the kingdom of Arthedain had more friendship with the Elves than the other two, who like Gondor appear to have started to become estranged from them. For it is noted that the other two kingdoms are ravaged but Arthedain holds out with "aid from Lindon and Imladris".

Did they become subkingdoms to Arthedain after their kings perished, or were they subkingdoms from the beginning and does the statement, "The chief of the lesser realms 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." suggest that there were actually more than three kingdoms? If not more than three how else can it be read than my reading that these two were the chief of the three lesser realms. Or can we take it that there is a mistake on Tolkien's part in the writing itself?