It is an irony that Taryn Power, a strikingly beautiful, open and friendly woman of 31, who sees the funny side of most things, knows her glamorous movie-star father, Tyrone Power, only through his screen roles in such films as The Mark of Zorro, Blood and Sand and The Razor's Edge. The daughter of Tyrone and his Mexican-born second wife, Linda Christian, Taryn says, "Apparently their relationship was on the rocks when I was conceived."

Taryn, who lived with her older sister, Romina, and their grandmother in Mexico City, was 2 when her parents divorced and 5 when Tyrone Power died. "I remember standing at the grave with my sister," she says. "A little old lady was sobbing, and I burst into giggles. We didn't realize what was going on."

Taken to Rome at about age 7, Taryn became aware that her mother spent much time in the downstairs apartment of English actor (and later her husband) Edmund Purdom. When Taryn heard rumors that her own father may have been bisexual, it didn't shock her at all. "In fact," she says, "it probably made my father seem more human."

Shepherded by nannies and tutors, Taryn was eventually sent to English boarding schools. "I really enjoyed learning," she says. "I used to play school in the summers." She excelled in both her studies and in athletics (javelin, tennis, a brown belt in judo). "By the time I was 15 I was doing the leads in most of the plays."

She was all set to enter the University of Leeds at 18 when, on a holiday in Spain, she was offered the star role in a Mexican film, Maria. "The idea of going professional terrified me," she admits. "At school you're safe because everyone is rooting for you." At her mother's suggestion, she consulted Sean Connery, a family friend. "He told me to give it a shot."

María was a hit with Latin American audiences and might have helped her career. Instead Taryn chose to use money from her father's estate to rent an apartment in Rome. "After all those years in boarding school, I needed to find myself," she explains. "I just cruised on his money, treated friends and turned down a lot of work."

Taryn also managed to fall repeatedly in and out of love. "I was always in search of a perfect romance. I wanted to have this Prince Charming for a mate—if there is such a person. I guess I've always been looking for Daddy." She was also proudly aware of the family's acting tradition, dating back to an earlier Tyrone Power, an Irishman born in 1797. (Her younger half brother, Tyrone Power Jr. [the IV], whom Taryn has never met, has a role in the upcoming film Cocoon.) In 1974 she seized the chance to play Louis Jourdan's daughter in The Count of Monte Cristo, shooting in Italy and starring Richard Chamberlain. "It was like a ticket to Hollywood," she says.

Taryn, then 21, arrived in Los Angeles in a fanfare of publicity over her friendship with Chamberlain. But, she admits, "There really wasn't a romance. I could never make Richard out." Despite roles in a cult film, Tracks, starring Dennis Hopper, and a Sinbad movie with John Wayne's son, Patrick, she considered moving to Mexico "where I had more of a name."

Instead, she stayed on in Los Angeles. There, in 1975, she met photographer Norman Seeff, 15 years her senior. For three years she acted as his girl Friday while she turned down movie roles "if there was any violence or sex," and even a soap commercial (and its $85,000 fee) "because that soap was 60 percent animal fat and I was then a vegetarian. I was extremely idealistic." Six weeks before the birth of their daughter, Tai Dawn, she and Seeff married.

For a while Taryn became a homebody. But when a serious friendship developed with rock 'n' roll musician Tony Fox Sales, son of comedian Soupy Sales, she confided in her husband. "We had an agreement," she explains, "that neither would have an affair without telling the other beforehand." Seeff moved out (they were divorced in 1982), and Sales moved in. Within two years, while Sales played lead guitar with the rock group Chequered Past, the couple had two children, Anthony Tyrone and Valentina Fox. "In fact," Taryn laughs, "I've been breast feeding for six years." She says she gives her children extra attention and love: "I seem to want to give them what I didn't have. My mother definitely wasn't conventional."

Right now Taryn wants to get back to acting. Recently she landed a part in a Matt Houston episode; to gain more exposure, she is currently appearing in Jackie Charge, a Los Angeles Equity waiver play. But the road back is not easy, a realization she shares with other offspring of the stars.

"I talked about this to Rory Flynn, Errors daughter, a year ago," Taryn recalls. "We said, 'It's bizarre. Here are you and me, and we're the daughters of who we are, and we can't get a job in this town.' " Maybe her name opens doors, Taryn concedes. "But I'm not my father and I know that. People expect a lot."