Mayu doesn't know, yet, but there is little chance she will ever leave this three-story children's home, where she has lived since her mother abandoned her when she was 3.

For now, the 8-year-old still senses possibilities. She sits in her corner of a shared bedroom, where her Hello Kitty dolls and teddy bears wait so reliably, and reads a postcard pulled from her backpack for the hundredth time. It is an orphan's dream, and Mayu savors it: a sweet, loving note from a couple who wants to adopt her.

We can't wait for our next visit, and until then, keep up your schoolwork, they tell her. Mayu picks up an orange crayon, smiling as she pushes her satiny black hair away from her face, and draws a bright, happy sun.

Chieko and Tadao Sato, who have no children after 10 years of marriage, desperately want to adopt her. They have brought her to their home, taken her shopping for holidays and filled her empty days with ice cream and love. Mayu loves being with them, and the director of the children's home believes it would be a wonderful match. But he knows it is a nearly impossible one.

Many people in Japan have a deep aversion to adoption, even though the practice has become a cherished way of creating families in much of the world. Japanese culture places a great emphasis on blood relations, so for many Japanese, someone else's child would never feel like true family.

There is a growing number of couples with attitudes like the Satos', but they are still the exception. Extended family ties are strong in Japan, and relatives often care for each other's children when the need arises. But when that is not possible -- for financial or other reasons -- many relatives would rather see these children in state homes than adopted by strangers.

As a result, Mayu and 25,000 others who live in Japan's 527 state-run or subsidized children's homes don't really belong to any family. They arrive at these homes because they were abandoned, neglected or abused by their biological parents. And there they live as Japan's invisible children, rarely discussed in public, and subtly discriminated against in private. In a nation where fitting in and being like everybody else is valued, growing up in a state home can make it hard to find a job, to get married or to just be a kid.

"Many Japanese with a conscience know we could take better care of these 25,000 children," said Yasuhiko Yuzawa, chairman of a nonprofit group of scholars and officials studying adoption. But as a rule, people feel no need to help them: "People think they are the responsibility of the state."

Many here defend Japan's system of caring for abandoned children. They say that Japan has far fewer children in state care than many other countries do, most notably the United States. And those children are generally well cared for, safe and guaranteed a high school education.

"Maybe it's a difference of culture," said Yoshio Murakami, a child care official of the Tokyo metropolitan government. "I can't say that being with an adoptive family is the best thing for the kids in these facilities."

Minoru Katoda, who runs the children's facility where Mayu lives, said the lost opportunities to create loving family lives for these children "is the worst part of Japanese obsession with blood relations."

An unusually outspoken advocate for children, Katoda allowed a reporter and photographer access to his children's home under the condition that it not be identified by name and that the privacy of the 50 children there be guarded. Tokyo government officials also allowed access to another facility where 110 children live. Many of those interviewed -- adoption advocates, doctors, social workers, and the children themselves -- believe that Mayu's predicament explains much about Japanese reluctance to adopt, and how that philosophy condemns thousands of children to a life in limbo.

In Japan, blood and money remain the chief motivators behind adoption.

Most of the people adopted in Japan are adult males, typically to carry on an heirless elderly couple's family name in exchange for their inheritance. Often, grandchildren are adopted as a legal way to dodge inheritance tax.

The Japanese koseki, official documents held by the government that mark birth, marriage, death and other milestones, have tremendous importance. Traditionally, divorce and adoption were seen as tarnishing these records, and, by extension, one's identity.

A law enacted in 1988 allowed young adopted children to have their birth family name erased from their koseki and replaced by their adoptive family's name. Before this, both names were listed, which essentially meant "adopted" was stamped in bold letters on this important record. The new law was to have made it easier for families to adopt nonrelatives without fear of stigma.

But things have not changed quickly. Many Japanese view their families as a privileged, almost sacred group. Western families, particularly American ones, are seen by Japanese as careless with that privilege. In their view, American families often start out of wedlock, end in divorce and often accept a stranger's child as their own through adoption. In Japan, millions of people see these actions as scandalous, or at the least, not to be discussed in public.

That is why the true number of adoptions between nonrelated families is impossible to find here. As is true with so many things in the complex calculus of Japanese culture, there is a public face and a private reality. An estimated 65,000 adoptions of unrelated children occur each year in the United States. The official number in Japan is about 600. The true number is believed to be significantly higher but still a fraction of what it is in most Western countries.

Many Japanese adoptions occur surreptitiously, with children handed off privately between families, sometimes with the help of a doctor, lawyer or broker who -- for a price -- will fake a birth certificate.

Akira Koizumi, a spokesman for the Japan Medical Association, dismissed the notion of doctors playing such a role, calling it "all hearsay."

But in interviews with young couples who want to adopt, many said they were instructed to turn quietly to obstetricians. The doctor who delivers unwanted babies in one room and witnesses the sadness of a miscarriage in another sometimes operates by the shadow rules, many here say.

Kazuko Yokota, who runs Motherly Network, a private adoption agency, said she believed doctors quietly help broker the adoptions of "hundreds of children" each year.

"It's all done in secret," she said. "Adoption is not the Japanese way." As a result, she said, some people go to great lengths -- even moving to a place where they are not known and feigning pregnancies with pillows -- to conceal an adoption.

There is a slowly growing willingness among young couples to adopt children. But even as the demand grows, the supply of available children is constricted by relatives who won't take in the children, but also won't let them go.

Relatives can hold out hope that the family will someday reunite. Quite often, there is just an emotional rejection of adoption as unnatural.

In Mayu's case, her aunt is her legal guardian. Mayu's mother was not married when she gave birth. After raising Mayu until she was almost 4, one day the mother dropped her off at a friend's and vanished. That was the last Mayu heard from her mother. Now her aunt, her mother's older sister, is her legal guardian, but no one at the children's home remembers the aunt coming to visit in four years.

But the aunt has made it clear she does not want Mayu to be adopted. Government social workers say the aunt has not explained why she is blocking the adoption, but, they say, her stance is typical. Despite repeated efforts, the aunt could not be reached to comment.

"Shame plays a big role in the Japanese mentality," Katoda said. "To let old people live in nursing homes is shameful. To let these children live in these facilities is shameful. But people think that perhaps even more shameful is to let them into the hands of another family."

So Mayu waits, in a home that is spotless and well equipped, full of television and Ping-Pong and other children -- but not a single picture of a mother or a father.

"In these facilities, the children have everything materially that they need," Katoda said. "But the facilities are no substitute for the most important thing: love."

Chieko Sato is waiting, too, hoping for a chance to plead her case directly to Mayu's aunt, to "demonstrate in front of her how much we love her."

Sato hates the stories she hears about how Mayu becomes so sad when other children at the home receive phone calls from relatives. The Satos have given Mayu a phone card she can use to call them.

"It makes us love her more," said Sato, 39, who sews handbags in her home for a living, while her husband, 40, works as a supervisor in a plastics factory.

Mayu and the other thousands of children in these homes are labeled in whispers on the playground as "the children from the facilities."

The homes have no budget for cram schools or private tutors, and so they do not spend after-school hours as the majority of their classmates do. They would have to pay for college themselves, so virtually no one goes. Typically, one day, between the ages of 18 and 20, they walk out on their own.

"It should be very simple," Sato said. "Mayu has no family to go to. We have no children. We love each other. . . . But it is not."

Special correspondent Shigehiko Togo contributed to this story.

CAPTION: Mayu peers from her room at the state home.

CAPTION: Mayu enjoys swinging with her best friend after a trip to a store. A couple yearns to adopt Mayu, but the girl's aunt, her legal guardian, says no.