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All three stars were nominated for six awards, but Ocean is up for three of the major categories including Best New Artist, Album of the Year and Record of the Year, which is awarded to the single.
In Ocean's case the single would be his soulful ballad "Thinkin' 'Bout You" from Channel Orange, his major-label debut released in July by Def Jam.
Fellow R&B crooner Miguel was nominated for Song of the Year with his track "Adorn" -- a category that the other three couldn't crack.
Kanye and Jay-Z are up for their collaboration album Watch the Throne in several categories. "Ni--as in Paris" is nominated as Best Rap Performance and Best Rap Song. "No Church in the Wild," which also features Ocean, is up for Best Rap Collaboration and Best Short Form Music Video.
On his own, Kanye was also nominated several times for the song "Mercy" off Cruel Summer, the G.O.O.D music collaboration released this year. The track is also up for Best Rap Song and Best Rap Performance.
The full list of nominees is available here.