MIAMI -- Nearly eight years after the battle over Elian Gonzalez divided South Florida, another Cuban child has become the center of a bitter custody fight.

A trial began Monday in family court to decide whether the 4-year-old girl's father can regain custody of his daughter or whether she should remain with the wealthy Cuban-American former sports agent and his wife who want to adopt her.

Miami-Dade County Judge Jeri Beth Cohen lifted a gag order Thursday on the parties -- propelling the case into the public and, possibly, political arena. The sides are keeping the girl's name secret.

The case began in 2004 when the girl's mother, Elena Perez, won the visa lottery to come to the United States with her son and daughter, each of whom has a different father. Both fathers agreed to allow their children to go, but Perez was hospitalized after a suicide attempt in December 2005.

The children were put in foster care and ended up with Joe Cubas, 46, and his wife. Perez agreed to allow them to adopt her son, now 13, but not her daughter with Rafael Izquierdo, 32.

Izquierdo, a farmer from the central Cuban village of Cabaiguan, said he wants to bring his daughter back to his family home, where he lives with his parents, wife and their 7-year-old daughter.

But before the custody case is resolved, a matter of whether Perez even gave consent for the state to take custody of her children must still be determined.

The Department of Children and Families on Friday revealed it couldn't find the documentation, so Izquierdo's attorney suggested Monday that it never happened.

"Since there is no order now in effect, I would ask you to immediately transfer custody to my client of his daughter," immigration lawyer Ira Kurzban asked the judge.

Cohen denied his request and instead wants the missing court order re-signed to prove that Perez did formally turn her children over to the state.

"It's not a conspiracy," Cohen said. "You know, we're not behind closed doors having secret hearings and in a conspiracy. No, no, no, no, no."

Izquierdo has complained that he has been allowed only 20 visits with his daughter and that often she is brought to him exhausted after a day of other activities. Still, "there is love between us," he said.

Perez seconded Izquierdo's request.

"Now that she's not going to her mother, she should go to her father," Perez said of her daughter. "Those are the two best people in the world to be at the side of a child."

Cubas said the girl, who calls him "Papi," shouldn't be separated from her brother and doesn't want to go back to Cuba.

"I don't believe this is a matter of where their better life could be provided," he said. "It is our belief, as is the wishes of the children, that they remain together and that's why we're here."

But Local 10 legal analyst Lee Stapleton said Izquierdo would likely regain custody.

"Blood is thicker than water, and family blood is always going to trump that blood between two countries," she said. "If the father wants his daughter, he is going to get her back."

The case is reminiscent of Elian, who was then 5 when he was found floating at sea on an inner tube on Thanksgiving Day 1999, his mother drowning with others during her attempt to bring him to the U.S.

His father didn't come to Miami until immigration officials ruled that the boy should return to Cuba, despite the objections of his Miami relatives and many Cuban exiles.

The debate ended after armed federal agents raided the Little Havana home of his uncle to seize Elian and send him to Cuba.