Peaches Geldof, who has followed in her late mother's footsteps in writing magazine and newspaper columns, will be the focus of the Sky One documentary "Peaches Geldof: Teenage Mind."

The 16-year-old calls herself a "shallow" teenager who just wants to be seen as cool. One body piercing got her grounded, but father Bob is "cool" with a more recent tongue stud, she said.

Peaches lives at home with her sisters, father and his girlfriend, French actress Jeanne Marine.

Mother Paula Yates, who died of a suspected heroin overdose five years ago, waged a bitter custody battle in 1994 when she left Geldof for INXS singer Michael Hutchence.

Peaches Geldof dates disc jockey Llewelyn Graves, the 21-year-old grandson of poet Robert Graves, who hopes to turn her into a rap star.