"His first name was that of an imaginary person we always had hanging around back when we had no one on our payroll," Gail told Victoria Balfour. "We'd snap our fingers and say, 'Ahmet? Dishes. Coffee, please.' He was also named after a giant pterodactyl that would have ravaged the world if the Japanese film Director Ishiro Honda hadn't destroyed it in 1957."
He has appeared in several feature films and television programs. In the late 1990s, he appeared on Channel 4 UK's The Adam and Joe Show, in a regular segment called "Vinyl Justice", in which hosts Adam Buxton and Joe Cornish, dressed as policemen, examined his vinyl collection for "criminal records". In 2000, he appeared in the film Ready to Rumble. With his brother Dweezil, he performed a cover of Britney Spears' song "...Baby One More Time" for the film's Soundtrack. Other appearances include hosting the TV shows Robotica and But Can They Sing?.
Zappa married Actress Selma Blair on January 24, 2004, at Carrie Fisher's mansion in Beverly Hills, California. Blair filed for divorce at the Los Angeles Superior Court on June 21, 2006, citing irreconcilable differences. In a statement to People, a spokesman for the couple said, "Selma and Ahmet have decided to divorce but love each other very much and will continue to be close friends".
Under Ahmet's direction, the trust proposed a trademark on the name Zappa, which would prevent Dweezil from using the name for commercial purposes without authorization. Since 2006, Dweezil toured with an act called Zappa Plays Zappa, playing his father's music. The trust sought to collect a fee of $1 from Dweezil for continued use of the name, as well as proceeds from merchandise sold at Zappa Plays Zappa concerts. In response to the trust’s action, Dweezil renamed his performance series “50 Years of Frank: Dweezil Zappa Plays Whatever the [email protected]%k He Wants — the Cease and Desist Tour.
Following the death of Zappa's mother, Gail, in October 2015, it was revealed that Ahmet and his sister Diva were given control of the Zappa Family Trust with shares of 30% each, while his siblings Moon and Dweezil were given smaller shares of 20% each. As beneficiaries only, Moon and Dweezil will not see any money from the trust until it is profitable—in 2016, it was "millions of dollars in debt"—and must seek permission from Ahmet, the trustee, to make money off of their father's music or merchandise bearing his name. The uneven divide of the trust has resulted in several conflicts between Zappa's children, including a feud between Dweezil and Ahmet over Dweezil's use of his father's music in live performances.