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Oksana Grigorieva, Mel Gibson

Giulio Marcocchi/Sipa Press

We haven't seen this much Mel Gibson around town since Braveheart was in Oscar contention.

For the second time in as many weeks, there was Mr. Lethal Weapon himself, sporting a pair of shades and a sheriff's deputy escort, walking into an L.A. court this morning for the latest round in his long-running custody drama with baby mama Oksana Grigorieva over their daughter, Lucia.

But Thunder Dome this ain't.

The ex-lovers arrived at the courthouse separately, both ignoring the crush of paparazzi—and each other—to talk with their attorneys as they went inside.

Since the case concerns a minor, the hearings are confidential and the press and public are being kept out.

Today's battle is believed to be focused on visitation—Grigorieva wants to keep him from having overnighters, while Gibson wants more daddy time. In fact, he prefers that he have full custody of the year-old Lucia.

Last week, the judge ordered Gibson, 54, to shell out $60,000 in child support to Grigorieva, 40.

Aside from their spat over their little girl, the former lovers are also embroiled in dueling allegations over domestic violence and extortion.

Sadly, this is one sequel that we don't think will have a Hollywood ending.