The Supreme Court is preparing to hear arguments on whether Anna Nicole Smith's estate should get part of the fortune left behind by her elderly Texas billionaire husband.

Lawyers for the deceased former Playmate plan to tell justices Tuesday her estate deserves some of the $1.6 billion estate of her late husband, J. Howard Marshall.

Marshall's will left nearly all his money to his son, E. Pierce Marshall, and nothing to Smith, who said her husband of 14 months promised to leave her more than $300 million.

But a federal appeals court sided with a Houston jury that said Marshall was mentally fit when he left his estate to his son and nothing to Smith.