Their first daughter, Fifi Trixibelle, was born on 31 March 1983, on 13 March 1989, and Pixie Geldof on 17 September 1990.
Yates first met Michael Hutchence in a 1985 interview on Channel 4's rock magazine programme The Tube.
She also appeared alongside friend Jennifer Saunders in 1987 for a spoof 'mockumentary' on Bananarama.During this appearance on The Tube, Yates was reportedly asked to leave Hutchence alone by the road manager of INXS when she walked up to him and said, "I'm going to have that boy." Yates was unmoved and began to show up at INXS gigs everywhere for the next few years, even bringing her daughter (Fifi Geldof).Yates wrote in her police statement that Hutchence was "frightened and couldn't stand a minute more without his baby." During their phone conversations on the morning of his suicide he had said, "I don't know how I'll live without Tiger." Yates also wrote that Geldof had threatened them repeatedly with, "Don't forget, I am above the law".I’ve met many charming men who have been very nice to me.I had a relationship with one of them for over a year.On 17 September 2000, on Pixie's 10th birthday, Yates, 41, died at her home in London of an accidental heroin overdose.The coroner ruled that it was not a suicide, but a result of "foolish and incautious" behaviour.Her aunt, Tina Hutchence, the sister of Michael Hutchence, was denied permission by the judge to apply for Tiger Lily to live with her in California.Since January 2008 her legal full name has been Heavenly Hiraani Tiger Lily Hutchence Geldof.A friend disclosed during the inquest that Yates had not taken illegal drugs for nearly two years, and the coroner, Paul Knapman, concluded that though the amount Yates had taken would not have killed an addict, as "an unsophisticated taker of heroin" Yates had no tolerance to the drug.Soon after her death, Geldof assumed foster custody of Tiger Lily so that she could be brought up with her three older half-sisters, Fifi, Peaches and Pixie.