Anna Nicole Smith's will was submitted to Los Angeles probate court Monday while Larry Birkhead sought to be named guardian of their daughter's estate.

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Smith's will was filed by Howard K. Stern, her companion and attorney, who also is named as the will's executor, People magazine reported.

The 2001 will left all of Smith's assets to her son Daniel, who died in 2006. She died in February, leaving behind her infant daughter, Dannielynn.

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Birkhead, who was determined by DNA testing to be the girl's father, filed his petition Monday in Los Angeles Superior Court, asking that he be named the guardian of the child's estate.

"What this means -- if granted -- is that Stern as the executor will have to deal with Birkhead on any matters pertaining to Anna Nicole's estate," says Allan Cutrow, a Los Angeles probate attorney.

While Stern listed Smith's assets at $710,000, her estate could be worth far more because of her long-standing claim against the estate of her late husband, J. Howard Marshall II, which is estimated at $1.6 billion.

A hearing was scheduled for June 19 regarding both filings.