This isn't a cadet branch, this is House Baratheon. Robert was the Lord of House Baratheon, not a cadet (younger son). Joffey was legally his eldest son and heir, not a cadet. Tommen stopped being a cadet when Joffrey died, now he's the (legal) head of House Baratheon.
In effect Robert moved the family's seat from Strom's End to King's Landing. Stannis' House Baratheon of Dragonstone and Renly's (new) House Baratheon of Storm's End were cadet branches.
We know that in reality the House is extict now because Tommen is Jamie's bastard, but offically it's not, and Tommen is it's Lord. It's seat and sigil has been changed but it's still the same House Baratheon.
- Its a cadet branch. Period. On a side note, you need to improve your English.--Gonzalo84 (talk) 09:46, July 19, 2015 (UTC)
Nope. Look up what "cadet branch" and "cadet" mean, my friend. It makes sense to have seperate articles for this wesbite given the situation but this is the same House Baratheon as "House Baratheon of Storm's End". First it changed seats (like House Targ did from Dragonstone) then Joffrey changed the sigil, that's all, it didn't become a new House. Tommen is it's Lord, he's not simultaneously head of two Houses just because he has two castles. Just as Littlefinger isn't Head of Two Different Houses just because he has Harrenhal and his nameless little keep in the Vale.
Pretend Robert didn't die so no war ever happened (and pretend he has a real son with Cersei if you like), Renly gets married and gets drunk enough to do it with his wife one night. He has a son and passes Storm's End on to him and Robert passes the throne on his trueborn son. Are you gonna call Robert and his House a Cadet Branch of his younger Brother's House just because the younger brothers house has the family's original castle? Of course not.
In-universe, it was never clear how Robert intended to handle the succession of "House Baratheon" distinct from the Iron Throne - did he intend to give Storm's End and the Stormlands to one of his brothers? Or, to his younger son Tommen? Or, for his son and heir to rule both the Stormlands and the Crownlands? We don't know.
The running theory is that he intended to keep the royal line and "House Baratheon" distinct. Technically this would make House Baratheon the cadet line as the younger branch, while "House Baratheon of King's Landing" would be the main one. But it's really treated as more of a "branch" than the main Baratheons (after Robert's death).
This is something we'd like to ask GRRM about.