“We do not reveal the location of smaller homes, because they are not protected by guards and fences, but the $3m-plus houses come with security you would not believe,” Goldsborough says. “We respect security, but privacy in this day and age is another issue.”

The housing cat-and-mouse game is nevertheless getting tougher, he says, as lawyers hold back from revealing details such as price until the last legal deadline. The stars, meanwhile, are becoming far more restless than they used to be: some, including the television chat-show host Ellen DeGeneres, seem to move every few months.

“Ellen, who hates us, seems to be worried someone is going to attack her,” Goldsborough says. “But she has pretty high security. Kelsey Grammer [star of the television series Frasier] and Nic Cage buy and sell as if houses are pieces on a Monopoly board. Some snap up houses anonymously, clean them up and sell them on without moving in — that’s called ‘flipping’.

“Celebrities love to buy houses from each other,” he adds. “It’s like it’s some kind of guarantee, so you can get long chains of celebrity ownership.”

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The actress Parker Posey, for example, bought a home in New York state from Tatum O’Neal. Lord of the Rings star Orlando Bloom, through his Kit Stone Trust, recently spent $2.75m on a Hollywood Hills house owned by an actor, Thomas Gibson, once famous for a television comedy called Dharma & Greg: there may be an omen there.

Old Tories used to sneer at interlopers who “had to buy their own furniture” rather than inherit it. David and Victoria Beckham may have committed a similar faux pas — despite taking advice from Tom Cruise, they bought an $18.2m off-the-rack new-build in San Ysidro Canyon, again in the Hollywood Hills, rather than choosing a house with a celebrity pedigree.

And in which name do the Beckhams trust? Hazelhurst. The name under which the property was bought is a reminder of the first house David bought for himself — on Hazelhurst Road, in Worsley, near Manchester.

When it comes time to sell — and that happens, on average, every three years with these properties — one estate agent estimates that a celebrity link can add 10% to an asking price (although a really juicy celebrity murder can add 15%). The big-name factor might help the rapper Kanye West shift a run-down Beverly Hills wreck — a “teardown”, in the parlance — for $8.7m, nine months after he bought it for $7.1m.

Not everyone plays the game, however. Lindsay Lohan is off the grid because she is renting rather than buying. “I am not grown up enough to buy anything yet,” she says, without jabbing a digit towards her former pal Britney Spears, who has been churning over houses at a loss since 2005 — quite a trick in LA’s boiling top-tier property market.

Even more amazingly, when, in August this year, the former Brookside actress Anna Friel plonked down almost $1.2m for a two-bedroom house in the Hollywood Hills, she did the deal under the name. . . Anna Louise Friel. Even more surreal than her Stateside TV hit, Pushing Daisies.

Sadly, that kind of open approach is not likely to catch on in the murky world that is buying a home in Hollywood.

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