To Elian Gonzalez's father, it's an open-and-shut case. He's the parent, and he says Elian should come home to Cuba. The U.S. courts ordinarily would agree with him; they have ruled that parents are free to raise their children as they see fit, without governmental interference. There are limits, however: parents may not put a child in harm's way. In Elian's case, the issue is whether returning him to a communist country would put him in danger. That's the hot topic in Miami, yet other parental-rights cases are springing up across the country.

This week some of the biggest questions come before the Supreme Court: Do parents have the right to limit their children's exposure to relatives, even grandparents? And do significant others--ex-boyfriends, former gay partners--have the right to seek visitation? In recent years every state has passed legislation saying grandparents--and, in some cases, virtually anyone--have that right. These laws have made it easier for the courts to overrule parents' decisions by lowering the standard to the more subjective "best interest of the child." In the case of Troxel v. Granville, the high court must decide whether lawmakers have gone too far.

In that case, the parents of two Seattle girls never married. The father, who lived with his own parents, occasionally brought the girls home for visits. After he committed suicide, the mother married, and her husband adopted the daughters. When the paternal grandparents demanded more access than the parents were willing to give, they ended up in court, and a judge granted monthly visits. The mother appealed the decision, saying the courts were trampling on her parental rights. The Washington State Supreme Court agreed. "They said the state should only intervene to prevent harm," says Carol Sanger of Columbia Law School. "There should be a compelling state interest."

A range of advocacy groups--from the AARP to Christian conservatives to gay activists--have filed briefs in the case, hoping that the high court will go beyond the narrow confines of the dispute to make a broader statement about the rights and limits of the modern family. But the ruling is unlikely to be the last word. "I think they will have to honestly acknowledge that this isn't one of those 'winner take all' conflicts, where one side is wrong and the other is right," says Lynn Wardle, a law professor at Brigham Young University. Determining a child's "best interest" is an elusive goal--in Washington or Havana.