Cadet Branch

"We are kin. Torbels of Dorkshire and Torbels of Estermont".
―Lord Eustace Torbel reminds Lord William Torbel of their blood ties.
They are usually created when a younger member of a noble house, who is not the current heir of the family seat, is granted lands and titles of his own. Bastards, if legitimized, or trueborn descendants of legitimized bastards, when granted lands and titles of their own, also found cadet branches.
Larger and wealthier noble houses such as the Torbels, the Lyoncasters, the Staffords, or the Byrch may have numerous younger cousins, but these are all part of the main house - albeit far down in the line of succession. When younger children or cousins form their own cadet branch, they become head of this new house, though the cadet branch is not considered as prestigious as the main line.
Strictly speaking, a "cadet branch" consists of only male-line descendants, in an unbroken chain from father to son - in which case the founding member was a younger son of another noble house. The inheritance systems in the Seven Kingdoms do not put as much value on descent through the female line. New houses have been formed from the female-line younger descendants of other houses, but their lineage is considered inferior compared to cadet branches who can claim male-line descent.