BY CAROL MARBIN MILLER

A 4-year-old girl living in Coral Gables is at the center of an international custody dispute between the United States and Cuba over who will raise her: her father who lives in Cuba and wants her back, or a family acquaintance who Florida child welfare administrators say is more fit.

Because of a secrecy order, the battle over the youngster has played out quietly in Miami-Dade County's juvenile courthouse in Allapattah. But three sources with knowledge of the case say state child-welfare workers have asked Circuit Judge Jeri B. Cohen to grant long-term custody of the girl to an acquaintance of the girl's family.

The girl, whose identity is being withheld by court and child-welfare administrators, was taken from her mother by the Florida Department of Children & Families about a year ago, sources said, after an investigation into charges that the mother's severe mental illness made her an unfit parent.

DCF also took custody of the girl's older, preteen brother. The children, who have different fathers living in Cuba, came to the United States legally two years ago. The boy's father agreed to surrender his parental rights, sources said, so there is no dispute about his staying in the United States.

The girl's father, though, is pressing to gain custody. His lawyer is Ira Kurzban, a prominent immigration attorney who has represented the Cuban government in the past.

Cohen, who presides over child-welfare, foster-care and adoption cases, has closed all proceedings in the case to the public and ordered all parties involved not to discuss it. It is not known when she will make a decision in the case.

A source said DCF administrators, who recently announced a new push to improve the agency's transparency, did not request that the proceedings be held behind closed doors.

THE BATTLE LINES

The Miami Herald has interviewed several people who have knowledge of the custody battle. Speaking on condition of anonymity, they outlined key aspects of the case.

DCF is represented in the case by Jason Dimitris, a former state and federal prosecutor recently named chief of staff for agency head Bob Butterworth. The family who is taking care of the children is represented by Alan I. Mishael, a prominent family and juvenile-court attorney and children's advocate.

There are similarities and differences between this case and that of Elián González, whose custody dispute made international headlines and sparked raw emotions in South Florida, where communities -- and even families -- were torn by heated arguments over where he belonged.

The main similarity: The new dispute involves a young child in Miami with a father in Cuba seeking custody, a case that once again could have political and emotional repercussions in South Florida and Havana.

The differences: Elián fled Cuba on a boat and was rescued at sea after his mother drowned. The mother of the girl in this case, who succeeded in bringing her child to the United States, is alive but was ruled unfit to care for her children. And there are no Miami relatives caring for the girl, as there were in Elián's case.

In Cuba, the mother of the girl had a short-lived relationship with the father, a source said. They were not married. The relationship had ended by the time the woman and both her children entered the U.S. two years ago.

Within about a year of the mother's arrival, however, she stopped taking psychiatric medication, and long-term parenting problems emerged, several sources said.

Following a call to the state's child-abuse and neglect hot line, DCF investigators took custody of the two children.

Like most parents who enter Florida's child dependency system, the mother was given a chance to improve her parenting skills and regain custody. She failed, however, and after losing custody of the two children is no longer involved in their lives, sources said.

Both children are now living with a Cuban-American family in a Coral Gables home.

As is customary in cases involving juveniles, The Miami Herald is not revealing the identity of the family that is caring for the children to protect the youngsters' privacy.

The girl's father has asserted his rights to the child. While the dispute has proceeded in court, a source said, he has been allowed weekly phone calls with his daughter.

NOT ALLOWED IN U.S.

The father has been denied permission by the U.S. State Department to enter the country to appear in court, a decision that has hindered his ability to fight for custody of his daughter. Though state law does not require his presence to grant him custody, many judges insist they meet and scrutinize potential caregivers before agreeing to give them custody.

DCF attorneys are arguing in court that the father in Cuba is unfit to have custody because he took no action to safeguard the daughter from her mother's abusive behavior while she lived on the island, a source said.

State workers have not suggested the father himself was physically abusive to the children.

At one point, the girl's mother told child welfare workers she would prefer that the girl live with her father in Cuba rather than in foster care, two sources told The Miami Herald.

To help the judge determine the father's fitness to have custody, Miami's private child protection agency asked an independent, international agency to conduct a review of the man's living conditions in Cuba. Such ''home studies'' are routinely conducted before a court decides whether to grant custody of a child.

Though the home study was generally positive, sources say DCF administrators remain skeptical because they fear representatives of the Cuban government were present during the evaluation and may have influenced its outcome.

''This was not a valid home study,'' a source said.

Seven years ago, Elián González was returned to his father in Cuba after he was forcibly removed from the home of his Miami relatives by federal agents. Sources said the history of the Elián case weighs on those involved with the new proceedings, and has much to do with the quiet and cautious handling of the dispute.

Miami Herald staff writers Scott Hiaasen, Frances Robles, Monica Z. Leal, Alfonso Chardy and Pablo Bachelet contributed to this report.