According to The Heirs of Elendil within The Peoples of Middle-earth, Volume 12 HoMe series, Elboron was born in the Fourth Age, and was possibly the only child of Faramir and Éowyn.

If this is indeed true, we can assume that he inherited the titles of Steward of Gondor and Prince of Ithilien. It is likely that Elboron was also the father of Barahir of Gondor, who recorded the "Tale of Aragorn and Arwen set forth in the appendices of LotR.
Encyclopedia entry originally written by Fíriel