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The Hollywood actress and her ex-partner have been embroiled in legal wrangling over Rosalind, four, since last 2014, when the businessman went to court to demand regular access to the youngster, who is nicknamed Luna.
While an initial deal was arranged in September, 2015, the New York Post's gossip column Page Six reports that "renewed tensions" between the pair have pushed them to continue the fight over their little girl.
The outlet reports that legal papers state the former couple could be facing off in Manhattan Supreme Court as early as December, 2016.
Read more: Uma Thurman’s ex suing for custody of their daughter
Details of the pair's previous agreement were never made public, but after signing off the deal, Justice Matthew Cooper said: "Both parties worked very hard to come up with an agreement that's in the best interests of your daughter... Everybody compromised a bit... I think it was all done to make one person happy and that one person is Luna."
Thurman and Busson, who also has two sons with supermodel Elle Macpherson, started dating in 2007, before getting engaged in June 2008. They split in 2009 before giving their romance another go and then broke up once and for all in April, 2014.
Busson's attorney Peter Bronstein had no comment when contacted by Page Six, while Thurman's representative has yet to respond.
Read more: Uma Thurman reunites with ex?
Thurman gave birth to Luna in 2012, raising eyebrows when her spokesperson revealed the tot's full name is: "Rosalind Arusha Arkadina Altalune Florence Thurman-Busson."
However, during an appearance on The Tonight Show Starring Jimmy Fallon, Uma explained the reasons behind the unusual moniker.
“(My daughter) Maya came up with the best excuse, which was that I probably wouldn’t get to have any more children, so I just put every name that I liked into the baby’s,” Uma laughed.
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