WASHINGTON, June 6 (AP)--Disputes between parents and grandparents over what's best for children are as old as time, but one such dispute has yielded a potentially far-reaching Supreme Court ruling. Never before has the nation's highest court had so much to say about something increasingly difficult to define: the "average American family." In a 6-3 decision Monday, the court said Washington State trampled on parents' "fundamental right" to raise their families free from government interference by enacting a law aimed at helping grandparents and others win visitation rights. Just what the ruling means for grandparents-visitation laws in all 49 other states remains to be seen, as does its impact for non-traditional families that split and turn to courts to referee battles over custody and visitation. Steven Shapiro, national legal director of the American Civil Liberties Union, hailed the decision as "a victory for nontraditional families nationwide ... particularly significant for single-parent families, lesbian and gay and low-income parents." Ruth Harlow, deputy legal director of the Lamba Legal Defense and Education Fund, agreed. "This is a very important decision for lesbian and gay families who are at the forefront of family law changes," she said. "The court adopted a sound middle course in this case, one that not only appropriately respects the rights of parents but acknowledges that no hard-and-fast rule should govern every single family dispute." None of the court's six separate opinions in the Washington State case mention such families. But Justice Sandra Day O'Connor, the main opinion's author, said, "The demographic changes of the past century make it difficult to speak of an average American family. The composition of families varies greatly from household to household." Justice Anthony M. Kennedy, in dissent, said the "conventional nuclear family ... is simply not the structure or prevailing condition in many households." Kennedy added a statement that advocates for non-traditional families are sure to seize on in future cases. "The importance of the familial relationship, to the individuals involved and to the society, stems from the emotional attachments that derive from the intimacy of daily association, and from the role it plays in promoting a way of life through the instruction of children as well as from the fact of blood relationship. "Some pre-existing relationships, then, serve to identify persons who have a strong attachment to the child with the ... motivation to act in a responsible way to ensure the child's welfare. ... In the design and elaboration of their visitation laws, states may be entitled to consider that certain relationships are such that to avoid the risk of harm a best-interests standard can be employed by their domestic relations courts in some circumstances." What's that mean? If up to Kennedy, even a fit and competent parent who objects to having someone else play a part in a child's life sometimes could be forced to do so--even if the person seeking visitation is not related by blood. Lawyers for adoptive parents and other non-biological caregivers already are giving the court's latest word on family law a thorough reading. That means it likely will not be the court's last word.