NASSAU, Bahamas -- A Bahamian court cleared the way Friday for Anna Nicole Smith's ex-boyfriend to leave with their baby daughter, rejecting an appeal by the mother of the former reality TV star.

The judges ruled that a U.S. court would likely have the final say in the custody dispute between Virgie Arthur and Larry Birkhead, who was confirmed as the 7-month-old baby's father after undergoing DNA testing.

Arthur was challenging a judge's decision this week to let Birkhead leave the island chain with Dannielynn. Her attorneys argued that Birkhead might not return as directed for another private hearing in the case June 8.

"I'm happy because this is nonsense really," Birkhead told The Associated Press outside the courthouse.

Birkhead, a 34-year-old Los Angeles photographer, picked up a revised birth certificate at the Nassau registry later Friday. A court ordered the name of Smith's last companion, Howard K. Stern, removed and the girl's last name changed to Birkhead, according to a copy obtained by the AP.

The three-member appeals panel noted that both Arthur and Birkhead wanted to take the child to the United States.

"So what is the problem, what is the fear? The child is going to the States anyhow, no matter who gets custody," Justice Emmanuel E. Osadebay said.

The court also ordered Arthur to pay Birkhead $3,000 in legal costs.

Smith, 39, died in February from an accidental drug overdose in Florida.

Stern, who has been caring for the girl in the oceanfront home he shared with Smith, patted Birkhead on the back after the ruling and said he was preparing himself emotionally to hand over custody.

"It's difficult for me, but since paternity tests made it clear that Larry was the father, I knew it was inevitable," Stern told the AP. "I just want Dannielynn to have a good life, and I'm confident Larry will give it to her."

Stern said he hopes to be involved in the girl's upbringing but that was up to Birkhead: "I'm not requiring written papers or court orders."

During the hearing, Arthur took notes with a flower-tipped pen in a spiral notebook. "I'm writing prayers," she told AP. "I'm talking to God."

Arthur left the courthouse after the ruling without commenting.

A lawyer for Birkhead, Emerick Knowles, said his client hopes to leave for the United States once he secures a passport for Dannielynn but plans to return for the hearing in June.

"He'd be silly not to," Knowles said. "He has every intention of complying with the law."

The girl could inherit a fortune if lawyers resolve challenges over her mother's estate in her favor. When she died of an accidental drug overdose in a Florida hotel room, lawyers were still wrangling over the estate of Smith's late husband, the Texas oil tycoon J. Howard Marshall II, estimated to be worth more than $1 billion.

Smith gave birth to Dannielynn only days before her 20-year-old son Daniel died of a drug overdose at her bedside.