Except for his grandparents Faramir and Éowyn, the details of Barahir's descent are uncertain. In The Heirs of Elendil (the ultimate basis for much of Appendix A), there is a single mention of a son of Faramir - apparently his only child - named Elboron. It isn't completely clear whether Tolkien meant this character to stand, but it seems reasonable to speculate that this Elboron was Barahir's father. This would in turn presumably see Barahir inheriting the titles of Steward of Gondor and Prince of Ithilien, though it should be emphasised that none of this is explicitly stated by Tolkien. (The Heirs of Elendil appears in The Peoples of Middle-earth, volume 12 of The History of Middle-earth).