British actor Jude Law’s daughter Iris is the new face of Burberry, having followed her brother Rafferty into modelling. Sofia Richie, the daughter of singer Lionel Richie, Kaia Jordan Gerber, the daughter of Cindy Crawford, and even Bob Dylan’s grandson, Levi, have all embarked on catwalk careers.

Michael Jackson’s daughter, Paris, turned up in the French capital this week for a photoshoot, adding her name to a bulging celebrity model roll call that includes the daughter of Oasis singer Noel Gallagher, the son of Isabelle Adjani and Daniel Day-Lewis, the daughter of Nastassja Kinski and Quincy Jones, and the sons of Sean Penn and Pierce Brosnan.

At Milan Fashion Week’s menswear shows, Prada seeks the naive and Marni bursts with hobo colour

You just have to look at the Kardashians to see how the model works, says Gachoucha Kretz, professor of fashion marketing at the HEC business school in Paris.

They have converted their reality television fame into fashion hard currency, with Kim Kardashian and her half-sister Kendall Jenner now established stars, their every wardrobe choice scrutinised on social media.

Brands hope to piggyback on “the popular fascination with these tribes and families”, Kretz says.

With no problem about name recognition “there is much less marketing to do”, she adds. “The associations are already created.”

With their Instagram or Twitter endorsements of their favoured brands, they become the ultimate “influencers” to help push demand.

Aged only 17, Brooklyn Beckham has nine million followers on Instagram. After two years as a model he has branched out into fashion photography, shooting an advertising campaign for Burberry this summer that made headlines around the world.

Even fashion’s biggest players are happy to play along with the family fame game. Chanel’s Karl Lagerfeld, for instance, has hired Depp, Smith and Jenner, and taken former supermodel Ines de la Fressange’s daughter Violette d’Urso as his muse.

“The tabloids and celebrity magazines love these famous families and that assures media coverage,” says Aurore Gorius, co-author of a 2015 French book Sons and Daughters of …, which casts a critical eye on the public’s fascination with this “phenomenon of elites reproducing themselves and blocking social mobility.

“These children have grown up under the eyes of the media and we are curious what will become of them,” she says.

Trends expert Cecile Poignant, who teaches at the New School Parsons Paris, says there has been a gradual push towards the “starification of childhood” over the past 15 years.

She said it began with photographer Annie Leibovitz’s famous front cover of a naked and pregnant Demi Moore for Vanity Fair magazine.

“For a lot of models and celebrities, the child has become something of a fashion accessory, a must have,” Poignant says.

But could the omnipresence of celebrity offspring now finally lead to a backlash?

Fashion student Marie Richaud says she finds it irksome that their fame “is not based on merit but family links. It excludes.”

Even so, the 25-year-old follows several second-generation celebs on Instagram even if “she doesn’t identify with them”.

“These children who seem to have had it all give people something to dream about. But at the same time they can just as easily annoy,” says Poignant.

“Do any of them have any talent or is their name enough [to succeed]? We will have to wait and see,” she adds.