Who owns The Rolling Stones' Catalog?

Does a record label own the rights to their music? people? a person?

"Klein acquired the rights to all of The Rolling Stones’ recordings from the 1960s and a couple from the '70s. Klein’s ABKCO (Allen B. Klein Company) label released the rarest of all Stones albums, Songs Of The Rolling Stones (1975). By the late '90s, some of the 60s albums were becoming hard to acquire on CD. Finally, in 2002, Allen’s son Jody Klein oversaw a re-mastering of the 60s albums, to much acclaim.

Klein bought the rights to music produced by Phil Spector, such as the Philles Records and Phil Spector International catalogues, in the 1980s."