Story Highlights• Bahamian court rules Larry Birkhead is the father of Anna Nicole Smiths's baby
• Howard K. Stern, listed as father on birth certificate, will not fight for custody
• DNA test is 99.99 percent certain, doctor says
• Smith's mother, Virgie Arthur, says she is happy with the outcome
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NASSAU, Bahamas (CNN) -- Former boyfriend Larry Birkhead was declared the father of Anna Nicole Smith's baby Tuesday, and Howard K. Stern, listed as Dannielynn's father on the birth certificate, said he would not fight for custody.
"My feelings for Dannielynn have not changed," said Stern, who was Smith's lawyer and live-in companion.
"I am not going to fight Larry Birkhead on custody. We're going to do what we can to make sure that the best interests of Dannielynn are carried out. And I'm going to do whatever I can to make sure he gets sole custody," Stern said outside the Bahamian courthouse where the DNA test results were disclosed. (Watch Stern express his disappointment )
When asked when Birkhead would get custody of the 7-month-old girl, who has been living with Stern in Nassau, Stern said he wanted there to be a "gradual transition."
Stern said Birkhead could come to the house any time and spend as much time as he wants with his daughter.
Another hearing is set for Friday to further discuss the custody issue, which involves Stern, Birkhead and Virgie Arthur, Smith's estranged mother who lives in Texas.
Arthur's attorney, John O'Quinn, told "Larry King Live" on Tuesday that Arthur would not seek any sort of guardianship for Dannielynn. Arthur and Birkhead will meet on Thursday, he said, in an attempt to reach an agreement regarding access to Dannielynn.
"Virgie is the grandmother, and we're going to respect that," he said.
Birkhead sits in a good position to take Dannielynn home soon, according to B. J. Bernstein, a defense attorney and CNN legal analyst.
"It's very difficult for grandparents ... to trump the natural, biological parent," Bernstein said.
Arthur said she was happy with the outcome of the results. "All I care about is the safety and well-being of my little granddaughter," she said. (Watch Smith's mom explain what she plans to do next )
Birkhead: I told you so
Birkhead was the first to share the paternity results with the public.
"Everybody, I hate to be the one to tell you this -- but I told you so," he said outside the court as he smiled and threw his hands into the air.
When asked what's next, he said, "I'm going to the toy store."
Crowds applauded in front of the courthouse as Birkhead made the announcement, and Birkhead teared up as he thanked his supporters. (Watch Birkhead be the one to say 'I told you so' )
A DNA test confirmed him as the father with 99.99 percent certainty, said Dr. Michael Baird, who performed the test and revealed the results to a closed session of a Bahamian court.
Baird told CNN's "Larry King Live" that a cheek sample was taken from Dannielynn on March 21 and tested on March 22. The DNA testing was finished March 26, he said, and the results were known to him and some members of his staff but were not made public until he opened the results in the courtroom Tuesday.
The court had ordered DNA testing to determine the father of the child, who has been at the center of a paternity dispute since she was born in a Bahamian hospital in September.
Birkhead, an entertainment reporter and photographer, said shortly after the baby's birth that he accompanied Smith to doctors' appointments until a "minor disagreement" took place while she was pregnant.
In September, Stern said on CNN's "Larry King Live" that he and Smith were confident he was the father, and "based on the timing of when the baby was born, there really is no doubt in either of our minds."
Zsa Zsa Gabor's husband, Frederic von Anhalt, also said he could be the father.
Dannielynn stands to inherit millions of dollars from the estate of Smith's late husband, oil tycoon Howard Marshall II. Until her death, Smith was involved in a legal battle over the inheritance.
The former Playboy Playmate died of an accidental drug overdose February 8.
After a protracted dispute over the burial of Smith's body, Stern and Birkhead began battling in Bahamian courts over the child, and a judge ordered that a swab be taken from the girl for DNA testing.
Stern then asked the Bahamas' Court of Appeal to block release of those test results, arguing that the judge had misinterpreted the law and his order invaded the girl's privacy.
Earlier this month, appellate judges questioned why Stern was raising legal claims after giving consent to the DNA swabbing.
Stern was ordered to pay $10,000 in court costs for the abandoned appeal.