A frowning woman crouches on top of a bookcase as a man in the living room below introduces another woman to a male acquaintance.

"That's my first wife up there, and this is the present Mrs. Harris," he explains.

James Thurber's cryptic cartoon points to a truth: Ex-spouses and ex-in-laws often stay in our lives long after we've officially ditched them. If not menacingly poised on the tops of bookcases, then at weddings, bar mitzvahs, graduations and funerals they mingle with those we've ditched them for. Marital upheaval is spawning multilimbed family trees with confusing arrays of step-cousins, half-brothers and ex-mothers-in-law crowding the branches.

"What used to be 'families' are oddly lost and blurred inside the constellations of the various new kinds of connection and relation," wrote Harold Brodkey in a recent New Yorker magazine piece about his granddaughter's complex family tree. "And no one yet knows what to make of these networks or of this new reality, except to live it..."

But cultural anthropologists say the way Americans view kinship depends on whom they want to call kin anyway. A simple enough question -- Who's related to whom? -- turns out to be the $64,000 one. The criteria for who's related to whom and what you call each other varies from person to person, as well as regionally. Throw step-kin into the confusion and more confusion ensues.

Who IS related to whom? My child is still kin to my ex-mother-in-law, so aren't we related by blood? Because my father's sister died, is the man she married no longer my uncle? Who's in and who's out? And what do we call one another?

What we call one another -- especially those intimate titles -- is so important that people have sued over it.

"I had a family in such a pickle that the biological father went to court to prevent the stepfather from being called 'daddy,' " recalled Bethesda psychologist Nancy Hafkin. "The judge agreed with him and ordered the kids to come up with another name for their stepfather."

Americans are uncomfortable with the prefix "step." It distances us. It sounds like "substitute" and "second rate." Indeed, one of the few new terms to emerge in familial matters -- "binuclear family" -- describes two households of a divorced couple still linked by children. It attempts to counteract the pain of disconnection, to extend our sense of family boundaries.

That's what the wife of Silver Spring etiquette consultant Forrest Winquest's ex-husband wanted to do. At her urging, the couple named Winquest godmother to their own baby. Winquest's sons delivered presents to their new half-sibling.

"It threw all the grandparents for a loop," said Winquest. "Their jaws dropped." Such a move establishes an accepted label for the connection that is otherwise unnamed between many such namelessly related families. But Winquest believes that advertising one's remarital status can have Thurber-like overtones.

"I was at a meeting where the group leader introduced his spouse to a whole group by saying, 'I'd like you to meet my new wife,' " recalled Winquest. "We all knew his former wife, and we cringed. It was like he was saying, 'There's an old wife and this here's the new model.' "

It should be enough simply to say, "I'd like you to meet my wife," according to Winquest, who advises corporations on manners and ceremonies. And an ex-mother-in-law should simply be "my children's grandmother." Why force others to contemplate your personal life?

Kinship -- based as it is on specific ties of blood or marriage -- ought to be more scientifically founded than etiquette. But Santa Cruz, Calif., anthropologist David Schneider -- regarded in his field as the authority on middle class kinship patterns -- found wide variation in whether specific connections were considered kin.

"It took years and years for anthropologists to agree with me that American kinship is a very flexible area with fuzzy boundaries," recalled Schneider. For instance, the seemingly straightforward question of whether one is a relative of an uncle's wife's cousins (when the uncle is "blood" kin and the aunt is "by marriage") turned out to be "one of those questions where there was a lot of variation in the people we studied," said Schneider.

To some subjects, whether a person was considered a relative or not depended on emotional closeness, frequency of personal contact, even common economic status. And Schneider's ultimate definition of what constitutes a relative leaves plenty of room for the variation, subjectivity and ambiguity.

"A person is a relative if he is related by blood or marriage and provided he is closely enough related (or is not too distant)," wrote Schneider, in his 1968 book American Kinship: A Cultural Account, which is still considered a standard text on the subject. But just how far blood can be thinned (third cousin, fourth?) or how many marriages such a definition can hurdle (am I related to my brother-in-law's brother's wife?) seems to be strictly a matter of one's personal taste for a particular individual.

"Do they live in the same place? Do they like the person? Does that 'relative' have something the other one would want?" asked Brett Williams, director of American Studies at American University. "The wonderful thing about American kinship is how we juggle it around, make it what we want it to be."

Williams' colleague Geoffrey Burkhart teaches a course called "Reinventing American Families" at AU, and has found the same flexibility among his students.

"When we discuss who's related to whom in class, we get some heavy arguments about who's a relative and who's not," said Burkhart. "Whether or not someone is considered kin is often a regional matter, or based on particular family traditions."

In some locales the child of one's first cousin is a second cousin, and in others, a first-cousin-once-removed. An "uncle by marriage" might mean one's spouse's uncle -- or one's parent's sister's husband. Is he still your uncle if she dies? Some subjects of Schneider's study felt not. Others said that if he's your living cousin's father, he's still your uncle. By this standard, wouldn't you be kin to your ex-mother-in-law if you're parent to her grandchildren?

As for step connections, anything goes. What we call each other has little to do with rules and much to do with what we want to call and be called.

Greenbelt resident Rose Clark and her fiance' want her children Brandon, 6, and Dana, 4, to call their future stepfather "daddy," even though that's also what they call their biological father.

"We want them to call him 'daddy' because we're planning to have children of our own," said Clark. "We thought it could be a problem if they keep calling him 'Joe.' We want all of them to call him the same thing." As for her fiance''s mother, who lives some distance away, "They call her 'Mrs. Maslow' now, and unless she plays a pretty big role in their lives, they might just call her 'Mrs. Maslow ... ' Maybe we'll find another name."

Jim Skellington, pastor of the United Methodist Church in Silver Spring, has been active in the Step Family Association of America. He thinks families about to become step families ought to sit down prior to marriage and decide what to call each other.

"It's unbelievable what folks coming in -- who are madly in love -- haven't talked about," said Skellington.

Winquest believes that until new families have become established, they don't know what they want to call each other. "The form comes first," she said, "then you name it."

But if Winquest and others favor a trend toward binuclear arrangements, Rockville social worker Coralie Adler has noticed that her stepchildren's teachers have been a bit surprised when Adler, her husband and his first wife show up together for conferences.

"They cover it pretty well, but some of them are embarrassed," said Adler, who also noticed awkwardness at her stepson's bar mitzvah. "It was somewhat uncomfortable deciding who'd sit where." It also complicated the photography, which required taking pictures of the child with his biological parents, and with each step-family grouping.

Brett Williams thinks we're in the midst of a revolution in how we view kinship. She recalled her own Texas childhood in the l950s.

"My father had died and my mother dated," she said. "And not having a father was considered pretty bizarre. Now my students routinely show up at graduation with two sets of parents."

Since Schneider discovered greater flexibility in who one chooses to call kin, it would seem our culture would more easily accept these new limbs being grafted onto our family trees. "But there's a real bind, a real paradox in the way we see step connections," said anthropologist Burkhart. "People want to insist step relationships are real kinship relationships. But the way American cultural concepts work, we always fall back on, 'No, he's my stepfather, not my real father.'"

Burkhart would eliminate the "step" term because it's a "qualification, stuck onto a more 'natural' relationship." And he argues that what once was natural is no longer -- because the old constructs simply don't apply.

"I think we've already reinvented the family," he said, "but we're reluctant to recognize it. We hold up old ideas about the way things are supposed to be." Students in his classes, he said, are often shocked to realize how many others in the class also have step relationships.

There's one kind of kinship connection, though, that most of us areeager to claim, no matter how circuitous the route. Celebrity kin. In his New Yorker essay, Brodkey describes a cousin who was formerly married to a woman related by blood to Ernest Hemingway.

"Are my granddaughter and I then related to Hemingway?" he asks.

"I think he is if he thinks he is," said Burkhart. "People can make choices about kinship relationships."

And having a tie to someone wholesomely famous "is a claim to sharing some good part of something natural," said Burkhart.

Schneider found several categories of kinfolk that are "sort of" relatives -- wake-and-wedding relatives (the ones we only see at the big formal occasions); kissin' cousins (distant kin whom we acknowledge as relatives by the fact we kiss them); and "shirttail" relatives. In the latter category fall those who ride into our lives on another relative's shirttails, so to speak -- a relative's relatives. Such kin may be rarely if ever glimpsed.

Let some distant connection achieve fame or fortune and watch the stampede of new relatives. But while we may be reinventing the family, we seem also to be yearning for an era when family was more easily defined. Family reunions are trendy. Genealogy has come back into vogue. And now popular Country decor emphasizes an apparent longing for the down-home and traditional family life, for a vision of log cabins in the snow. But can such a fantasy accommodate the endless number of kinfolk and sort-of kinfolk we're finding on our new family tree?

"People have to make up their own rules {and} not worry so much about kinship," said Burkhart. "What matters about these people is that we have feelings for them. That ought to introduce a lot of flexibility."