#There are possible candidates.
Note: if there were any who felt that their claim was strong enoughBy known descent alone, theythere would have challenged the rule of the Stewards prior to Aragorn's arrival and Eärnur's death (26 of them). No challenges were made during Denethor's rule. Not only that, any possible candidate would have also challenged Aragorn's claim to the crown.be Seeing that none resisted Aragorn's claim, you could say that there was no one who had as strong a claim as Aragorn's on the CrownDírhael grandfather of Gondor.Aragorn
This being said, it doesn't mean that there wasn't anyone who would classify as a candidate.
In all honesty, theThe only known (male) person to have his ancestry to a near King explicitly described would be Dírhael grandfather of Aragorn (explained below). Faramir and Imrahil are of high lineage, yes, but they are not stated to have been of the line of the Kings. For the purpose of clarity I will still add them into this answer.
###Candidates through known descent:
- ###Dírhael grandfather of Aragorn
As mentioned, in terms of lineage, there are other candidates.
###Possible candidates:
- ###Dírhael grandfatherDúnedain of Aragornthe North
He is one of the northern kindred of the Gondorians, being descended from a Chieftain of the Dúnedain in Arnor.
He is noted here to be the only person to have been explicitly described as an ancestor of the royal line. Faramir and Imrahil are never stated to have been of the line of the Kings- just that they are of high lineages.
He is noted to have been descended from Aranarth:
His son Arathorn sought in marriage Gilraen the Fair, daughter of Dirhael, who was himself a descendant of Aranarth.
This would make him of a high lineage, but being a descendant of the Kings of Arnor, he wouldn't have as much popular support with the people of Gondor as compared to the first 3 candidates I have mentioned. This is a completely similar case with his ancestor Arvedui the Last King; he was rejected the Crown of Gondor because he wasn't popular.
He would be placed fourth after Faramir and Imrahil and the Dúnedain of the South because:
- He isn't popular in Gondor
- ###Dúnedain of the North
They would be placed last after Faramir, Imrahil, Dúnedain of the South and Dírhael because:
Therefore, the factors that give one the right to the Kingship would be: having pure blood (arguably high lineage as well) and being popular in Gondor. These are the reasons why Aragorn was made the King, excellently explained here.
Note: if there were any who felt that their claim was strong enough, they would have challenged the rule of the Stewards prior to Aragorn's arrival and Eärnur's death (26 of them). No challenges were made during Denethor's rule. Not only that, any possible candidate would have also challenged Aragorn's claim to the crown. Seeing that none resisted Aragorn's claim, you could say that there was no one who had as strong a claim as Aragorn's on the Crown of Gondor.