Sir Paul McCartney and Heather Mills have failed to reach agreement over a financial settlement in their High Court divorce case.
The hearing took place behind closed doors
The settlement will be decided at a later date by Mr Justice Bennett after he reserved judgement on the case.
It has been suggested the financial settlement could break records.
Divorce experts have suggested that, based on recent cases, Ms Mills could walk away with £60m of Sir Paul's estimated £825m.
That would make it the biggest settlement of its kind in a British court.
The current record rests with businessman John Charman who was ordered to pay £48m to his ex-wife last year.
Ms Mills, who has been representing herself throughout the hearing, smiled at waiting reporters as she left court.
Sir Paul, 65 - thought to be rehearsing for Wednesday night's Brit Awards where he will receive a special prize for outstanding contribution to music - was not in court on Monday.
Mr Justice Bennett's judgement, due in the next few weeks, will be binding on both parties and may never be known to the outside world.
Any financial settlement will not be made public unless the case goes to the Court of Appeal.
But his judgement could be challenged there if either side is unhappy.
Ms Mills would have put forward a case of where she wants to live, what homes she needs, what expenses she's got and what security she needs
Alan Kaufman, divorce lawyer
Under those circumstances, the case - which has so far remained behind closed doors - would become public, with all arguments in the public domain.
Divorce lawyer Alan Kaufman told the BBC News website that Mr Justice Bennett would have "a hard job" in deciding what was a fair proportion of Sir Paul's wealth to give to Ms Mills.
Factors that could be taken into account include the short duration of the marriage and the fact that most of the wealth was created before the marriage, he said.
"But how far does he go? He's got to look at what are her actual needs.
"Ms Mills would have put forward a case of where she wants to live, what homes she needs, what expenses she's got and what security she needs."
The judge would also have to bear in mind that, if either party were unhappy with his judgement, it would have to "look sound and well-principled so it's not subject to criticism in a higher court if one of them decides to appeal", Mr Kaufman added.
"So all those things are the things going through this poor judge's mind," he added.
Ms Mills, 40, who lost part of a leg in a road accident in 1993, married Sir Paul in June 2002, four years after the death of his first wife Linda from breast cancer.
The couple, who have a four-year-old daughter Beatrice together, announced the end of their marriage in 2006.