Mel Gibson is set to appear in a Los Angeles County Court Monday seeking custody of a child he had with Oksana Grigorieva, a celebrity Web site said.

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TMZ.com said Gibson is appearing because he wants the judge to see how serious he is about getting full custody of their daughter, Lucia.

The couple's domestic disputes have been widely reported, and Grigorieva appeared on Larry King Live on Wednesday, where she said Gibson hit and choked her while she was holding the baby.

TMZ.com said Gibson thinks his wife is unstable, and he wants her to have only supervised visits with the child for six months.

Gibson also said Grigorieva is hurting the infant by conducting what he considers a public smear campaign based on lies to extort money from him, the report said.

The pair's domestic problems blanketed news reports this summer when an obscenity-laced recorded telephone conversation was leaked to the media.