The Beatles assigned their publishing rights to Northern Songs, a company created by Beatles manager Brian Epstein and music publisher Dick James in 1963. The Beatles (particularly John Lennon and Paul McCartney) were soon earning so much money from songwriting royalties, record sales, concert performances, and merchandise licensing that they were losing over 90% of their income in taxes, and they were advised to find a way of receiving their revenue in the form of capital gains rather than income (the former being taxed at a much lower rate), such as selling their song rights or putting their money into a public company. The Beatles opted for the latter route, and Northern Songs went public on the London Stock Exchange in 1965. Initially, Lennon and McCartney each retained 15% of the shares, George Harrison and Ringo Starr held 1.6% between them, Brian Epstein's NEMS company was assigned 7.5%, and Dick James and Charles Silver (Northern Songs' chairman) retained a total of 37.5%. In 1969, however, the Beatles lost a buyout bid for control of Northern Songs when Dick James and Charles Silver sold their share of the company to Sir Lew Grade, head of Associated Television Corporation (ATV).
In 1984, ATV's 4,000-song music catalog was put up for sale, and Michael Jackson (who had coincidentally been introduced to the benefits of song ownership
by Paul McCartney himself) eventually outbid all other prospective buyers for it, including Paul McCartney, who wanted to buy back the rights to the Beatles' songs but was apparently unable or unwilling to raise enough money to pay for the thousands of other songs in the ATV catalog as well. So, for $47.5 million, Jackson acquired the publishing rights to most of the Beatles songs. (The four songs issued on the Beatles' first two singles — "Love Me Do" b/w "P.S. I Love You" and "Please Please Me" b/w "Ask Me Why" — were not part of the package since they were published before the formation of Northern Songs, and the rights to those songs are now controlled by McCartney's MPL Communications. ATV also did not own the rights to George Harrison songs published after Harrison's songwriting contract with Northern Songs expired in 1968, but they did hold the rights to various other Lennon-McCartney songs not recorded by the Beatles.)
Another key point here is that although Michael Jackson received 50% of the royalties generated by Beatles songs by virtue of his ownership of the publishing rights, Paul McCartney and John Lennon (and Lennon's estate, now that he's dead) have always received their 50% songwriter's share of the royalties for all Lennon-McCartney songs. Neither ATV's nor Michael Jackson's acquisition of Northern Songs changed that, and Michael Jackson did not receive royalties that would otherwise be going to the Beatles had he not acquired the publishing rights to their songs (except that, obviously, if Paul McCartney had managed to outbid Jackson for the publishing rights to the Beatles catalog, he and Lennon's estate would be splitting 100% of the royalties rather than 50%).
As a closing note, we should mention that Sony Corp. paid Michael Jackson $95 million in 1995 to merge ATV with Sony and form Sony/ATV Music Publishing, a 50-50 joint venture, so it's probably more correct to say that Jackson owned half the rights to the Beatles catalog.