Sir Paul McCartney and Heather Mills have failed to reach an agreement over a financial settlement in their divorce case.
The judge ruling in the case, Mr Justice Bennett, will now impose the settlement after the pair were unable to resolve their differences over the appropriate financial conclusion to their marriage.
It is thought that an eventual settlement could be the biggest in British legal history, surpassing the £48 million paid by businessman John Chambers to his ex-wife in 2007.
The judge's decision will remain secret unless either of the parties challenge his ruling, at which point proceedings will move into public domain in the court of appeal.
Ms Mills, a former model, smiled at reporters as she left Monday's proceedings at London's high court while Sir Paul - believed to be rehearsing for Wednesday's Brit Awards - did not attend.
The pair separated in 2006 after four years of marriage and have a three-year-old daughter named Beatrice.
Forty-year-old charity campaigner Ms Mills is thought to be representing herself in court, having dismissed her legal team.
Legal experts have argued her decision could be hugely risky, given the quality of Sir Paul's legal team, which includes Fiona Shackleton, who represented Prince Charles during his divorce from Princess Diana.
Sandra Smith of law firm SAS Daniels told the AFP news agency: "She must be mad to do it herself.
"She will be up against one of the finest legal teams in the world, led by Nicholas Mostyn QC.
"I just wonder what is behind it all. She is obviously asking for a lot more than Sir Paul is prepared to offer."
Ms Smith added: "She will have to show that Sir Paul has the means to provide her with a settlement allowing her an independent existence, taking into account the loss of her own career and the upbringing of their daughter."