Larry Birkhead is the father of Anna Nicole's Baby

Here Full name is now Dannielynn Hope Marshall Birkhead, and as she grows into the poor little rich girl that she seems fated to be she can at least be 99.9 per cent certain of who her father is.

DNA test results released in the Bahamas yesterday established that Dannielynn's father is 34-year-old Larry Birkhead, a Los Angeles freelance photographer, very occasional television actor and consort of Anna Nicole Smith over several years.

In asserting his paternity, Mr Birkhead had previously claimed that Dannielynn was conceived in Las Vegas on New Year's Eve 2005. Mr Birkhead was jubilant after yesterday's announcement. He waved and gave a thumbs up to the crowd outside the Bahamian court.

"I hate to be the one who told you this but … I told you so," he said. "My baby's gonna be coming home pretty soon. Nothing's been determined yet but parentage, and I'm the father. It's been a long road, and I'm happy to have this behind me and to be able to start a life with my daughter."

Mr Birkhead's paternity was established by DNA expert Dr Michael Baird, who said the results were "99.99999 per cent" certain.

Now seven months old, Dannielynn lost her mother on February 8 when Anna Nicole Smith died of an accidental overdose of prescription drugs. Subsequent toxicology tests showed that Smith, 39, had taken nine different medications and a powerful sedative.

At the time of her death, Smith was in the midst of a complicated array of lawsuits contesting her $US500 million ($A606 million) inheritance from her former husband of 14 months, Texas oil tycoon Howard Marshall. The pair were married when Smith was 26 and Mr Marshall 89.

In her will, Smith had named her son Daniel as heir. But Daniel, 20, died of a drug overdose in September last year. This left Dannielynn, as the sole heir to an estate in which not only the source of the wealth has died, but also the two bitterly opposed litigants — Smith and Howard Marshall's son Pierce, who died last June. Court action on the division of the estate is still pending.

With yesterday's announcement, Mr Birkhead has at least entered the vault. Whether he can open it may be decided later this week, with further court hearings to resolve Dannielynn's custody. That is being contested by Smith's mother, Virgie Arthur, in a Florida court.

The loser in the case is Howard Stern, Smith's lawyer and companion, who was one of several to claim paternity.

Mr Stern had said he and Smith planned to wed on February 23. Mr Stern has had custody of Dannielynn at a house in the Bahamas since Smith's death.