There have been many different stories concerning Sir Ector and his relationship in the Arthurian legends. One that is the most well-known is the one that Victoria mentioned in her post with,

Sir Kay was also the son of Ector, and Kay and Arthur grew up together as stepbrothers.

Most of what the current legend is based on traditions written down around the 12th and 13th-centuries by Geoffrey of Monmouth in his Historia Regum Britanniae which was originally written in Latin by the author and another version written in French known as Le Conte du Graal written by Chreitien de Troyes. Both authors claim that they recieved thier information from earlier unknown sources, but are not clear on which sources they recieved this from. The only way for us to find out about these in retrospect is to scour all of the possible resources there are on the subject.

One such source that we can cull information from is the Saga of Kulwhch and Olwen where the unknown author states,

At that time, in the fortress of Kelliwic in Kernyw, there was a lord whose name is now lost. He had a son and a daughter. The daughter was called Anna and the son Arthur because he was very ygly and looked like a bear. Two other children came, in accordance with custom, to be brought up with the lord’s children. One was called Gywar, the other Kai son of Kynyr.

This passage is interesting because we see the reciprocal of the latter accepted tradition of the myth. Rather than Arthur being made foster brother to Kai, Kai is made a foster brother to Arthur. It would appear that the medieval authors changed the story to make it more of a pauper to king story rather than what the earlier versions suggest. In other later traditions, Ector is said to be the father of Peredur.

An interesting pasage comes from the Welsh Mabinogion where Ector is called Evrawc and is the legendary founder of York.

Earl Evrawc owned the Earldom of the North. And he had seven sons. And Evrawc maintained himself not so much by his own possessions as by attending tournaments, and wars, and combats. And, as it often befalls those who join in encounters and wars, he was slain, and six of his sons likewise. Now the name of the seventh son was Peredur, and he was the youngest of them.

While these theories are not close to being fully developed yet, they are interesting possibilities and should be investigated in more detail.