: Lines of succession among the Eldar and other races ran to male heirs by way of male descent. Daughters were not heirs, and neither was a son of a sister or a daughter.

Except, of course,1) that Dior is called Thingol's heir in places ("Elwing...daughter of Dior, Thingols heir..."), note the punctuation making this descriptive of function not a name. Also Dior himself states "...I am the heir of King Elwe...". 2)Idril Celebrindal, Turgon's daughter, is refered to as Turgon's heir. 3) Maeglin, son of Aredhel, sister of Turgon, is implied to at least have the possibility of being Turgon's heir.

: We know this was the law among the Noldor: when Turgon died the High Kingship passed to his fairly distant nephew Rodnor Gil-galad (son of Arothir Orodreth) rather than to his grandson Earendil. The latter was not of male descent.

Earendil was seven years old. Also I can say that the High Kingship passed to Gil-galad because he was the eldest male of the House of Fingolfin (this was, as I recall, one of the reasons Maedhros gave up the Kingship to Fingolfin and in the process, for other reasons as well, disinherited his own House from the title.

: We know that this same law applied on Numenor (before they changed it). That is explicitly stated in Unfinshed Tales.

: The same law seems to have applied among the Dwarves. Dain Ironfoot seems always to have been Thorin Oakenshield's heir. There is no suggestion that Fili (the elder of Thorin's sister-sons) was ever considered to be his heir. Indeed, in The Hobbit Thorin introduced Fili and Kili as "sons of my father's daughter," a circumlocutous introduction to say the least. He seems to emphasizing clear that they were only his nephews, not his heirs.

The Naugrim are not Eldar and have differing laws and customs. Fili and Kili were both killed defending Thorin so neither could have inherited. Dain then became the closest surviving male relative and the most powerful to boot. Thorin's circumlocution is part of his speaking style he was being exceedingly formal.

: It is my view that Dior was not Thingol's legal heir. I tend to agree with MM that Dior's refounding of Doriath was his own decision.

But nontheless done as Thingol's heir.

: However the law may have allowed for sister-sons or daughter-sons to become heirs if there were no heirs of male descent. We know that happened among the Rohirrim twice, and also among the Stewards of Gondor. But they are Third Age instances, a long way removed from the Elder Days.

The Rohirrim are not Eldar. The stewards are not Eldar nor are they kings.

: If we accept what I call "Celeborn and Galadriel Scenario C" (CGC). That is, the scenario presented in LOTR Appendix A and in The Silmarillion. In which Celeborn is said to be a prince of the Sindar of Doriath (specifically a grandson of Elmo, a brother of Elwe Thingol). Then Celeborn may well have been Thingol's legal heir. But if so, why is that fact never mentioned? Another reason to reject CGC perhaps?

The conception of Celeborn as a Teleri of Aman came from an unfinished work that was 'philosophical' rather than 'historical'
in nature. It was also greatly at variance with works published in JRRT's lifetime ie the LOTR and RGEO, and JRRT would have undoubtedly felt bound to stay true to the already published facts. Even so Celeborn being Telporno was a late account and he was Thingol's nephew while Dior was Thingol's heir during the time of the various writings on the subject of Doriath etc.