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An Australian woman claims that Oscar-winning director Steven Soderbergh, 48, fathered her baby daughter -- and now she's suing him for child support.

Frances Lawrencina Anderson's paternity suit claims the Erin Brockovich director helped alleviate medical expenses during her pregnancy, and a DNA test showed he was the father of the girl she had in August.

In the lawsuit, filed in a state court in NYC Wednesday, Anderson alleges that Soderbergh "has acknowledged he is the father of the child verbally."

According to the Huffington Post, Soderbergh's lawyer declined to comment on the lawsuit; his manager didn't immediately return a telephone call.

Soderbergh has been married to novelist and former E! News personality Jules Asner since 2003.