04/02/2007 AT 01:50 PM EDT
Anna Nicole Smith's partner, Howard K. Stern, has dropped his attempt to block the release of DNA test results that could reveal who is the father of Smith's baby daughter.
The turnaround came after a round of skeptical questioning by the Bahamas' three-judge Court of Appeal made it appear that the court was was going to reject his appeal, the Associated Press reports.
All three judges pointed out that Stern was late in filing his challenge and should have raised his objections before the Supreme Court ordered DNA testing
in the paternity challenge filed by Larry Birkhead.
Birkhead, a former boyfriend of Smith's, claims that he is the father of the infant, Dannielynn, born in the Bahamas in September. He met the child
for the first time in late February. Stern is listed as the father on Dannielynn's birth certificate.
But Justice Emmanuel E. Osadebay noted that Stern had agreed to DNA testing and then waited a week after the sample was taken to file his legal challenge.
Dannielynn's DNA was tested March 21, but so far the results have not been revealed.
A Supreme Court hearing in the paternity case is scheduled for Tuesday, but Bahamian law prohibits lawyers and officials from discussing the case or even revealing what the hearing is about, according to the AP.
The baby, whose full name is Dannielynn Hope Marshall Stern, stands to inherit millions from the estate of Smith's late husband, Texas oil baron J. Howard Marshall II, who died in 1995. Smith, who died Feb. 8
, had been battling his family over the estimated $500 million fortune.