Noble Oligarchie. Dukes losing Capitals.

I played as the Tulleys and created the Noble Oligarchy. When a Leader dies he loses the capital of his duchie and gives it to his Sucessor. This happens with every succession.
e.g. Tullys lose Riverrun to Mallisters. Mallisters lose Seagart to Freys and freys lose the Twins and so on.