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MIAMI, Florida (CNN) -- A Florida judge said Friday he is not sure courts in his state -- or in California -- have the authority to order Anna Nicole Smith's DNA samples turned over for testing in a paternity dispute.

Larry Birkhead, one of several men claiming to be the father of Smith's 5-month-old daughter, Dannielynn, filed legal papers requesting the samples. The 5-month old child, Dannielynn, was born in and lives in the Bahamas.

"As you begin the staircase, step one is jurisdiction," Broward Circuit Judge Lawrence Korda told Birkhead's legal team at a brief hearing.

The attorneys provided Korda with several legal opinions that they said bolster their argument that he has jurisdiction in the case.

Birkhead filed his paternity suit in California before Smith's death.

His attorneys claim the California judge is asking the Florida court to release Smith's DNA samples -- collected by the Broward County Medical Examiner -- to Birkhead's expert.

Korda said, however, he questions "how California can give me jurisdiction to domesticate their order when they may have no better jurisdiction than I do."

Birkhead's attorneys also want Korda to order DNA samples from Dannielynn, but the judge said he would deal with that issue after jurisdiction has been established.

Birkhead was in court on Friday morning, but not Howard K. Stern, Smith's lawyer-turned-paramour who is named as the father on the baby's birth certificate.

Birkhead's lawyers sought an emergency hearing. But Korda noted that the paternity issue does not carry the same urgency as the question of who receives Smith's embalmed remains.

In contrast to the sometimes bizarre court proceedings of the past week, which legal analysts have called a circus, Korda handled the hearing in a no-nonsense manner.

At one point he told Birkhead's lawyers, "I'm not wide open for questioning such as you may be used to."

He refused to hear from attorneys for Smith and Stern, who also claims to be Dannielynn's father.

"This is a paternity case filed by Mr. Birkhead ... and I'm still trying to find out what your standing is," he told them.

Attorney Susan Brown maintained afterward that Korda "most definitely has jurisdiction over the DNA samples, which California has already asked him to provide to the DNA expert."

She added, "We also believe, reading the California orders together, he has jurisdiction to order the testing of Dannielynn, who is the bottom line in this case."

Brown said she expects a decision from Korda possibly by Monday.

"This is about Anna Nicole Smith running from Larry Birkhead (to the Bahamas)," Brown said. "Because Larry Birkhead is the father of this child, and we should be permitted to prove it, either in California, here or in the Bahamas."

The paternity hearing came a day after another judge, Larry Seidlin, granted custody of Smith's body to her infant daughter's guardian.

On Thursday, Stern and Birkhead said they agreed Smith should be buried in the Bahamas, next to her son Daniel. The men made the announcement a few minutes after Seidlin tearfully awarded custody of the body to Richard Milstein, guardian ad litem for Dannielynn. (Watch the judge's emotional ruling )

A motion to stay Seidlin's order was filed Friday by attorneys for Virgie Arthur, Smith's mother, but an appeal won't be filed until Monday, the attorneys told CNN. Arthur wanted custody of Smith's remains so she could bury her daughter in Texas near other family members.

Smith died February 8 in a Florida hotel. The cause of her death still is unknown.

Broward County Medical Examiner Joshua Perper predicted the appeal would be dismissed in short order.

"Probably in a day or two there's going to be a final decision," he told reporters. "So we'll be able to make the arrangements."

Seidlin made no secret of his wishes: "I want her buried with her son in the Bahamas," he told a stunned courtroom. "I want them to be together."

Perper, who carried out the autopsy, said it will likely take up to 14 days before he can determine the cause of death.

"At this time, we don't have any evidence of foul play," he said about Smith's death.

Thursday's ruling capped several days of unusual courtroom proceedings that touched on child custody and paternity, though the issue at hand was limited to the disposition of Smith's body. Some called the proceedings a circus.

Before ruling, Seidlin told the parties in the case, "I feel for you, I absolutely feel for you."

"I've reviewed absolutely everything. I've suffered with this," Seidlin said.

He addressed Smith's mother several times as "mama" and told her and the others he was trying to reach an equitable decision. (Thursday's testimony)

Smith married Texas oil tycoon J. Howard Marshall II in 1994 when he was 89 and she was 26. She had been fighting his family over his estimated $500 million fortune since his death in 1995.

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