Which house has the most cadet branches? Like after the rebellion there were three branches of house Baratheon; Kingslanding, Dragonstone, and Stormsend. And now house Tyrell has a branch at bright water keep (on paper) but which house in westeros has the most official cadet branches?

Are we talking official cadet houses or extended family pure and simple?

Because the Tyrells have Garth the Gross’ line, Ser Moryn’s line down in Hightower, Quentyn’s line, and Victor’s line, in addition to a bunch of Maesters. And it’s a rare Tyrell who doesn’t have at least two children.

 However, if we’re going by official cadets, I think the Lannisters win it with the Lannisters of Lannisport, the Lannys of Lannisport, the Lannetts of Lannisport, the Lantells of Lannisport, and any number of unimaginative relations.