It’s official: Leon Black’s Apollo Global Management owns CKX, the company that billionaire Robert F. X. Sillerman created to capitalize on TV hits including American Idol and So You Think You Can Dance, and the licensing rights to Elvis Presley and Muhammad Ali. The final price came to about $510 million or $5.50 a share. In CKX’s heyday, in May 2005, the stock sold for close to $30. Apollo will have its hands full: CKX must negotiate a new Idol deal with Fox, and develop plans to fix up Graceland, Presley’s former home that’s now a tourist attraction. Sillerman, who amassed his fortune trading radio stations and concert venues, now is building Function (x), an investment firm that plans to focus on media and entertainment ventures with special attention to digital and mobile technologies.