@farmerman,
The Bern Museum only gets those paintings, which are definitely not looted.
(Besides that, one of Gurlitt's cousins claims to be a heir, too.)
Rosenberg had kept his paintings (about 160) in a bank safe in Libourne in 1940. He and his family then fled via Spain to the USA.
The Nazis sometime later them ... and somehow they came to the
Galerie nationale du Jeu de Paume in Paris. In 1944, the Paris art dealer Gustav Rochlitz bought them (he was friendly with a lot of Nazis, including Goering).
It's not known how Hildebrand Gurlitt got the Matisse, but when in 1956 his widow had inherited his collection - it was obviously there.
Rosenberg resp. his heirs got some of his paintings back - 62 were lost. (now 61)