LONDON, England (CNN) -- Paul McCartney and his estranged wife, Heather Mills, met Thursday at a London courtroom for the start of what could become the most expensive divorce battle in British legal history.
The couple, who have a four-year-old daughter, Beatrice Milly, arrived in separate vehicles at the back of the Royal Courts of Justice in central London.
They left in separate vehicles seven hours later without saying anything, The Associated Press reports.
It's not known if they reached an agreement.
Around two dozen reporters and cameramen had assembled around the rear gates of the family section of the building, an expression of the intense media interest the case has generated, as the couple went inside for the first hearing on the suit.
Mills, 39, was shielded from photographers by a man holding a large black cloth as she entered the building. McCartney, 65, arrived at court dressed in a dark gray suit, waving to the crowd from his car.
Once inside, the pair made their way to a private court room to work out details of a settlement expected to cost McCartney in excess of $100 million in total payouts, according to some legal experts.
The ex-Beatle hopes to avoid a public, and potentially very embarrassing, court battle in the wake of the couple's separation last year after four years of marriage.
The couple, who first met at a charity event, insisted at the time the split was "amicable" despite widespread reports of a tempestuous relationship between the former Beatle and Mills, an ex-model.
The final settlement is likely to be a single lump sum followed by annual payments to Mills until the couple's daughter reaches 18 years-old, and could include a privacy clause barring either party from speaking publicly about the split.
Estimated at over $100 million, the divorce settlement would be the highest in British legal history but would still fall short of other celebrity divorces.

The singer Neil Diamond lost half his fortune -- an estimated $150 million -- when he separated from his wife of 25 years, Marcia Murphy, in 1994, citing irreconcilable differences. Diamond later said his ex-wife was "worth every penny."
Steven Spielberg paid Amy Irving $100 million after she successfully contested their prenuptial agreement following nearly four years of marriage. E-mail to a friend ![]()
All About Heather Mills • Paul McCartney • The Beatles
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