House Baratheon of King's Landing is a cadet branch of the original House Baratheon of Storm's End. It is the new and current royal house of Westeros since the defeat of and exile of the Targaryen dynasty following Robert's Rebellion.
Their seat is the Red Keep, in the city of King's Landing, and their domains are the lands ruled directly by the Iron Throne, the Crownlands. With the death of King Joffrey I Baratheon, the current King of Westeros and head of the house is King Tommen I Baratheon.
In reality, House Baratheon of King's Landing became a puppet house of House Lannister the moment Joffrey I ascended; all three of Robert Baratheon and Cersei Lannister's supposed children were actually the products of an incestuous relationship between Cersei and her twin brother Jaime.