The Beatles' music rights are distributed to a few different owners. Are you talking about performance rights or publishing rights?
The rights to the performances belong to Apple Corps, which is technically a partnership owned by McCartney, Starr, and the estates of Lennon (i.e., Ono) and Harrison (i.e., Olivia, his second wife). Those rights are licensed by Apple to EMI.
https://en.wikipedia.org/wiki/Apple_Corps
The publishing rights to the music depend upon the song. The items published through Northern Songs (UK) and Maclen Music (US), which is the majority of the catalogue, were owned by ATV, but those rights were sold to Michael Jackson in 1985. Subsequently, Michael Jackson sold 50% of the rights in the ATV catalogue to Sony, which is why the songs are currently published through Sony/ATV Music.
Of the Lennon/McCartney songs not published through Northern/Maclen (mostly songs from the first album), McCartney has purchased the publishing rights to them all, so the rights are held by his MPL Communications. Rights to the Harrison Beatles songs published in 1969 and 1970 ("Something", "Here Comes the Sun", "For You Blue", etc.) are held by the Harrison estate; and rights to the Starr songs published then ("Octopus's Garden") are held by Starr.
https://en.wikipedia.org/wiki/Northern_Songs
