French financier Arpad Busson, former fiancé of actress Uma Thurman, has filed a petition for an emergency custody order in Manhattan Supreme Court to obtain custody of their two-year-old daughter, Luna.

Full details of the case were not disclosed since custody battles are usually held in matrimonial court, where records are automatically sealed.

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But New York Daily News learned that the case was assigned to Manhattan Supreme Court Justice Matthew Cooper, who only handles divorce, custody, and child support cases.

The "Pulp Fiction" star and the 51-year-old Hedge fund manager have been dating on and off since 2007.

The couple got engaged in 2008, but they ended their engagement twice - in 2009 and most recently last April.

Their only daughter Luna, whose full name is Rosalind Arusha Arkadina Altalune Florence Thurman-Busson, was born in July 2012.

Thurman has two other children with her former husband and fellow actor Ethan Hawke, namely Maya, 16, and Levon, 12.

The 44-year-old actress married the "Reality Bites" star in 1997, but broke up in 2003.

Their divorce was finalized two years later with Thurman getting the custody of their children.

Busson, on the other hand, also has two sons, Flynn, 16, and Aurelius, 11, from a previous relationship with Australian supermodel Elle Macpherson.

Since his split with Thurman, Busson is reportedly dating British actress Kristin Scott Thomas, who starred in romantic drama "The English Patient."

For Thurman's part, recent rumors have linked her to "Kill Bill" director Quentin Tarantino, but those claims were immediately shot down.

A source told Page Six that the two "are longtime friends and that's it."

Meanwhile, a spokesperson for Thurman told ET that "It is unfortunate that this very private discussion regarding Mr. Busson's visitation rights and his participation in decision making has been made public."

"However, we are optimistic that a fair agreement for both sides will be reached out of court," the insider added.

TagsUma Thurman, Arpad Busson, child custody, Luna, Manhattan Supreme Court, Ethan Hawke, Elle Macpherson, Kristin Scott Thomas, Quentin Tarantino