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Mel Gibson, Oksana Grigorieva

Michael Kovac/FilmMagic

It's time for Mel Gibson to put up or shut up.

After months of negative headlines over those controversial leaked tapes and reports of alleged domestic violence, the disgraced star is scheduled to turn up at a mediation center in Los Angeles to be deposed in his ongoing custody battle with estranged girlfriend Oksana Grigorieva.

The deposition, set to get under way at 9 a.m. PT, is likely to last all day. Oksana's lawyer, Daniel Horowitz, previously told E! News that Gibson's legal team was expected to file motions to have it postponed, but as of press time the deposition is still on.

According to Horowitz, the Russian musician has also been relying heavily on the expertise of Martin Garbus, a First Amendment attorney from New York who's currently searching for an L.A.-area apartment so he can give this case his utmost attention.

Garbus has mapped out a strategy to help Grigorieva win full custody of the couple's daughter, Lucia, who just turned 1 Oct. 30.

Horowitz hinted that Team Oksana may very well play the infamous recordings for Gibson and discuss his alleged mental health issues in an attempt to paint him as too unstable to care for their child.

"He's admitted he's manic-depressive before," the legal eagle tells E! News.

As for Grigorieva, he adds that "she's not really nervous."

"Oksana had dinner with Marty Garbus last night and they talked about other aspects of the case," Horowitz said. "She was relaxed and smiling."

Grigorieva was deposed on Friday and "did great," Horowitz noted. "She was calm and just told the truth."

And in a bit of strange timing (or good planning if you're the Biography Channel), the lawyer also said he watched Mad Mel: The Rise and Fall of a Hollywood Icon, which aired over the weekend.