If the frequency with which her megawatt mug peered out from magazine covers around the world is any indication, last month was a good one for Heidi Klum. From men’s mags such as Arena, on the cover of which she saucily flaunted some upper-bum cleavage in a teeny-weeny bathing costume, to the New York-based high-society bible Town & Country, in which she smiled sweetly in a pink Dior by John Galliano evening gown, Klum has been everywhere this summer.

The tabloids chronicled her afternoon strolls in Los Angeles parks with her husband, Seal, and their three children. Entertainment Weekly, in the States, welcomed another instalment of Project Runway, her reality-television designers’ competition, for which she has earned an Emmy nomination. And, at 34, she has never been more in demand. Last year, she was the third-highest-paid model in the world, according to Forbes, behind Gisele and Kate Moss.

For her latest trick, she is modelling handbags for the high-street accessories brand Accessorize. On set at the shoot, Klum’s mother – wearing rolled-up jeans, a T-shirt and a pair of Birkenstocks (from her daughter’s collaboration with the company) – shows up with Klum’s youngest child, Johan Riley Fyodor Taiwo Samuel, born in November. “How’s my little bunny?” Klum chirps in slightly German-accented babyspeak, drowning the buggy in her blonde locks. “What a cute bunny.”

After numerous calls from the Accessorize people regarding what could and couldn’t be discussed with Klum (“no personal questions at all”), it’s a surprise when Klum puts her baby’s feet in her mouth before recounting, on the record, the stroll she took with her husband through downtown Manhattan yesterday. It’s almost shocking when, during the break for lunch (“I wonder if they brought this schnitzel in for me,” she teases, taking a hearty chunk of fried mystery meat off the catering buffet), she chats freely about her three children. You have to admit it’s charming. To the cast and the crew, and in the pictures that are taken today, Klum emerges – as Michael Kors, the American fashion designer and her fellow judge on Project Runway, puts it – as a beguiling and witty “bombshell next door”.

Which brings us to the question many found themselves asking this summer, as the model stared out from the covers of their glossy beach reading: how has this bubbly, busty sometime blonde stayed relevant for quite so long? Is it her ever-ready smile? The curvy figure? Sheer photogenics? Does it have something to do with her outgoing sense of humour? Or her willingness to do anything for a good picture (like clutching a pillow to her crotch for the Arena shoot) and a good time (she wore a giant apple costume to her Hallowe’en party last year, requiring her to arrive in an open-top car because she couldn't fit in a limo)?

According to Kors, it’s down to her ability to play normal. “Only in your wildest dreams does the girl next door look like her,” he says, “but her personality makes you think that indeed she does live next door.”

Klum’s supermodel package certainly seems to contain more than, as one former model agent put it a few years back, “a talentless German sausage”. Douglas Perrett, a casting director in New York (who blogs about models on his site, www.coacd.blogspot.com), agrees. “The model life span today is hardly three months, let alone three years,” he says. “But Heidi filled out $10 bras and panties for Victoria’s Secret, and – boom! – endorsement deals and brand power. Now she is doing television deals, magazine covers, editorial and runway.”

While the foundations of the Klum package are built on a big smile and an even bigger chest, that’s just the start. She’s a consummate multitasker, what the designer Zac Posen calls a “prototypical powerhouse woman”. She models (her deal with Victoria’s Secret is reportedly worth £12.6m), she presents (Project Runway is in its fourth season, and she hosts Germany’s Next Top Model) and she runs design projects (there’s the jewellery line and the Birkenstock collection). She also manages to raise her kids and keep up a phenomenal social schedule. After a string of high-profile musician boyfriends, she had her first child with the Euro-playboy and Formula One boss Flavio Briatore. Then she fell in love with the soulful crooner Seal, and popped out two more kids.

Fact is, Klum comes from the supermodel generation of girls who wanted to be just as loud as the clothes they were wearing. Some may discount what she actually says, but few will argue with her work ethic. The thing that keeps Heidi Klum in the minds of readers, writers, advertisers and editors is Heidi Klum herself – that big ol’ Heidi package – and she knows it.

The next phase of Klum’s life will keep her legend alive. “Being a mother has changed my life completely,” she says at the shoot, alternately cutting into her schnitzel and looking at herself intently in the mirror, making sure her new fringe is in place and the fried food hasn’t smudged her lip liner. “Before, it was all about me. Now it’s about the children.” In contrast to her old model-on-the-go lifestyle, Klum prefers to keep her schedule in check. “I try to stay in one place and make everyone come to me,” she chirps. “Like, my agent called and said he had a job in Australia that’s really good money. But I don’t care. I don’t want to go. I have to make a rhythm for my children here and in LA.”

While she’s happy to be voluble about her children, she’s more secretive on the subject of Seal. All she’ll offer is “I met him three and a half years ago” and “My husband is always gorgeous”. Presumably, that applies to the time she dressed him in drag, as a biblical Eve to her forbidden apple for Hallowe’en. Further inquiries about him provide briefer answers. Summer plans? “Going on holiday with my husband, just the two of us.” Where? “I’m not telling you.” Well, will it be hot or cold? “Just somewhere amazing.”

The final facet of the Klum package is business, or what Kyle Hagler, her booker at the IMG agency in New York, likes to call, in his American way, her “never diva-like ultimate professionalism”. Klum doesn’t disagree. “It’s important to know what you’re putting your name on,” she says. “I think that’s why things I’ve done have been so successful. If it’s not real, then it won’t be good.” She admits that when she first signed on to do this campaign, she “wasn’t too familiar with Accessorize”, but by the end of the shoot, she is managing a convincing job of selling the products, even insisting to Hagler that a small hat be added to her contract (“It would be so good for this 40th-birthday party I’m going to”), as well as a bag she lent her name to, but didn't help to design.

After she has gone through every pose – from reclining on a fake-fur rug with a handbag on her bosom to kneeling in a floppy hat – the modelling industry’s renaissance woman says she needs to get back to her babies. But before she goes, she makes it clear – in case we were wondering – how unlikely it is that this gorgeous girl next door will be taking her focus off the worlds of fashion and entertainment any time soon.

Draped seductively in a director’s chair, she fixes me with those hazel eyes and says, enthusiastically but sternly: “I have more ideas for TV shows.” Then, turning around and surveying her domain, she adds: “I think that the entertainment world is my thing. It’s been my lime-green convertible Bug’ good to me so far.”

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