AceShowbiz - A lawyer representing Mel Gibson's ex-girlfriend Oksana Grigorieva has vowed to fight a search warrant which will allow cops to seize the singer's computer - insisting the device contains files of a personal nature. The "Braveheart" star has been locked in a bitter fight with his former partner over custody of their baby daughter Lucia, following their split earlier this year.

Cops are also investigating allegations Grigorieva attempted to blackmail the star by asking for money to keep explosive tapes of their bitter arguments private. The judge presiding over the case has now signed a search warrant which will allow members of the Los Angeles County Sheriff's Department access to Grigorieva's personal computer.

But an attorney representing the singer is determined to fight the order, because the computer contains personal pictures of Grigorieva breastfeeding her baby daughter, as well as her unheard music recordings. Grigorieva's attorney Daniel Horowitz has scheduled a court hearing for Thursday, October 21 and will ask Judge Scott Gordon to limit the warrant to include only audio recordings, photos, emails and text messages which are linked to Gibson.

In legal papers, obtained by TMZ.com, Horowitz states, "These are communications between Mel Gibson and Oksana Grigorieva that are rather normal, civilized and reflect discussions between adults who are genuinely attempting to provide for the financial welfare of their child." Grigorieva denies attempting to extort money from Gibson in any way.