NEW YORK (AP) — Uma Thurman and ex-boyfriend Arpad Busson are facing off in a New York City court over their 4-year-old daughter.

The Oscar-nominated actress and the financier were in court Friday for the start of their custody trial. It concerns visits and other issues.

Thurman and Busson dated for several years and were engaged for a time. Their daughter, Luna, was born in 2012.

A court-appointed psychologist testified Friday that the parents now have an acrimonious relationship.

Thurman has two children with ex-husband and fellow actor Ethan Hawke. Busson, nicknamed "Arki," has two children with model Elle Macpherson.

The custody trial continues next week.

Thurman was nominated for an Oscar in 1994 for best supporting actress in "Pulp Fiction." She's starred in the "Kill Bill" films.