IF THERE'S A GENE THAT makes you stage struck, it's obviously not recessive. For Barrymores and Fondas and Redgraves, Douglases and Sheens, an attraction to the limelight seems to be in the blood. Talent, however, must have its own chromosome, as each generation of celebrity spawn proves. Some make the leap to stardom; some flounder. For every Jamie Lee Curtis, there's a Desi Arnaz Jr.

But they all seem to get cast -- at least once. Could it be connections? Sure. Yet the tidal wave of showbiz kids now hitting Hollywood is delivering some of today's finest young actors and, especially, actresses.

Gwyneth Paltrow, daughter of Blythe Danner and TV producer Bruce Paltrow, barely has to audition anymore. ''I wouldn't say that's an overstatement,'' says casting director Billy Hopkins, who placed Paltrow, 22, in three of her five upcoming films, Seven, Emma, and The Pallbearer. ''Right now, in that age bracket, Gwyneth just sort of has the pick. Anybody who says it's because she's so-and-so's daughter, they're jealous.''

Liv Tyler, daughter of Aerosmith's Steven Tyler and model Bebe Buell, made a splash in her father's video for ''Crazy.'' She'll appear in this month's Empire Records and later this year in Heavy. Just 18, she recently wrapped a starring role in Bernardo Bertolucci's Stealing Beauty opposite Jeremy Irons and will be seen in Woody Allen's as-yet-untitled 1996 release. ''She's gonna have a huge career,'' says a CAA agent who's admired Tyler from afar. ''She has a movie-star presence.''

Mira Sorvino, 26, daughter of Paul and Lorraine, is following up strong notices from last year's Quiz Show and Barcelona with a leading role in this fall's Mighty Aphro dite, Allen's new comedy. ''She's on all my lists,'' says casting director Ronnie Yeskel. ''She's gonna get her big break someday, and that'll be it.''

Ashley Judd, 26, daughter of Naomi and sister of Wynonna, gained acclaim in the 1993 festival hit Ruby in Paradise and is currently playing a drug addict in Smoke. She'll be seen next in Heat as Val Kilmer's wife, and in the movie version of John Grisham's A Time to Kill. Ruby director Victor Nunez says she's been smart to be choosy. She photographs ''like Ingrid Bergman.''

Then there's Schuyler Fisk, 13, Sissy Spacek's daughter, who's starring in The Baby-sitters Club; Angelina Jolie, 20, daughter of Jon Voight, who makes her debut in Hackers next week; and 16-year-old Clementine Shepherd-Ford, Cybill Shepherd's daughter, who was considered for the Lolita remake.

Certainly, nepotism exists. Would Sofia Coppola have entered our consciousness without it? When Kathlyn Bening Beatty and Scout LaRue Willis come of age, they'll have no trouble getting auditions. ''If a famous person has a kid who is interested in acting, of course you will meet them,'' says Hopkins. ''You do get asked and you do do it.''

Just growing up in the business helps too. Paltrow's break came out of the blue when, while waiting to see The Silence of the Lambs with Steven Spielberg and family, he offered her the part of Wendy in Hook.