EXCLUSIVE: Last minute hitch in Uma Thurman's custody battle with ex-fiancée Arpad Busson as the actress blows off court appearance to read for a play

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After another last minute hitch, the bitter custody battle between Uma Thurman and ex-fiancée Arpad Busson over their four-year-old daughter Luna almost ended Thursday when the pair agreed to a tentative settlement.

But Thurman, 46, did not make it to court to sign off on the agreement, opting instead to read for a Broadway play called The Parisian Woman.

Eleanor Alter - Thurman's attorney - said over the phone, however, that the agreement was 'confirmed' and that she was headed to a Broadway studio this afternoon so that Thurman could sign the paperwork.

Manhattan Supreme Justice Matthew Cooper will formally allocute the Oscar-nominated star at 9:30am Friday to make sure she understands the process.

Uma Thurman's x-fiancée Arpad Busson showed up in court Thursday to sign off on the custody agreement over their four-year-old daughter but the actress went to a reading for a Broadway play 

Thurman was all smiles a she left  Manhattan Supreme Court following Tuesday's '98 percent' agreement

If all goes as planned, it will bring to an end the rancorous two-year battle between Thurman and 53-year-old Busson over how and where their little girl, Luna, should be raised.

The details of the agreement have not been made public and neither parent has commented on the outcome.

On Wednesday, Thurman was seen taking her daughter Luna to Cirque du Soleil’s musical theater show Paramour. 

And on Thursday, she read for The Parisian Woman, a Broadway production by Beau Willimon - a political comedy about power and corruption set in Capitol Hill.

Thurman and her chiseled financier ex aired their dirty laundry in an eight-day custody trial with Busson accusing Thurman of mixing prescription drugs with alcohol to cope with stress.

She fired back claiming Busson was a neglectful dad, an 'angry boyfriend' and suggested he once confided in her that he was addicted to prostitutes.

On Monday Justice Cooper unexpectedly declared he was hopeful of reaching a settlement, going so far as to claim the couple's differences were '98 percent resolved'.

The former lovers also bickered over a $1.5 million engagement ring that Thurman allegedly refuses to return to Busson

The sparring legal teams looked drained but determined to finish the job when they arrived at New York County Supreme Court this morning after talks ran late into Wednesday night.

'This has to be for real,' Justice Cooper warned them before inviting both teams to speak in chambers. 'If this deal happens you can sleep all weekend.'

He emerged several hours later and told the court 'I'm delighted to say there is going to be an agreement,' adding that he was happy for Thurman, Busson but 'most of all the child'.

French-born Busson, wearing a smart black suit and tie, spoke briefly to confirm that he understood the terms of the 39-page settlement.

Asked if anyone had forced him to sign, he casually said, 'yes', before correcting himself: 'no, your honor.'

Busson's attorney Peter Bronstein asked what would happen if Thurman backed out and Justice Cooper replied: 'If Miss Thurman did not sign the agreement it would be totally null and void and I would disregard it.'

But he added: 'The 0.2 percent was a little tough but I'm assured that Miss Thurman will sign.'

Luna's court appointed attorney Virginia Lopreto also signaled she was happy with the deal.

Thurman and Busson dated for seven years and were briefly engaged until their March 2014 split, two years after the birth of their daughter, whose full name is Altalune Florence.

She been living in New York with Thurman and her two children from actor Ethan Hawke but Busson wants her to spend more time at his homes in London and the Bahamas.

A psychologist warned last week that the parents now have an acrimonious relationship and it was hard to question that verdict given the slew of allegations that followed.

 The court heard she gave it back after their engagement broke off for the first time in 2008 but he presented it to her a second time after Luna was born on July 15, 2012

Busson testified last week that he sought custody of Luna because he wanted to be more involved in her upbringing and have a greater say over her school and healthcare.

He also wants her to be raised a Catholic although Lopreto poured scorn on his claims to lead a religious way of life, pointing out he has three children outside of marriage.

The businessman admitted in court that he once confessed to Thurman that he paid another student to take an exam at his prestigious Swiss boarding school.

But he denied ever admitting he was addicted to prostitutes or that he was ever violent toward another former girlfriend, the supermodel Elle Macpherson, the mother of his two teenage sons.

Busson conceded that he once offered to give up any claim toward Luna in exchange for giving up child support but said any suggestion he abandoned her was a 'complete lie'.

The court heard he handed Luna back to her mother after a recent visit with matted hair and dirty clothes but Bronstein claimed Thurman caused a 'major drama' every time he tried to see his daughter.

He said his client paid $30,000 for business class seats last summer when Thurman agreed to take Luna to see him in London only to find out she wanted to go because 'her lover' was in town.

Bronstein also asked Sara Weiss, the court-appointed psychologist, to confirm Thurman was consuming a dangerous cocktail of 'serious psychiatric drugs' and alcohol but the judge cut off the questioning.

The former lovers also bickered over a $1.5 million engagement ring that Thurman allegedly refuses to return to Busson.

The court heard she gave it back after their engagement broke off for the first time in 2008 but he presented it to her a second time after Luna was born on July 15, 2012.

Busson said Thurman suggested it should be put into a trust for her children but he thought it 'shocking' that Luna would only receive a third of its value.

Thurman, who was nominated for an Oscar in 1994 for best supporting actress in Pulp Fiction, had already been excused from today's hearing because of her acting commitments.

Alter said the actress would not be commenting ahead of tomorrow’s session and declined to reveal any details of the settlement.