Buster appears briefly onscreen, but mainly narrates these live-action segments, which show real children and how they live. One episode featured a family with five children, living in a trailer in Virginia, all sharing one room. In another, Buster visits a Mormon family in Utah. He has dropped in on fundamentalist Christians and Muslims as well as American Indians and Hmong. He has shown the lives of children who have only one parent, and those who live with grandparents.

Marc Brown, creator of "Arthur" and "Postcards From Buster," said in a statement: "I am disappointed by PBS's decision not to distribute the 'Postcards From Buster' 'Sugartime!' episode to public television stations. What we are trying to do in the series is connect kids with other kids by reflecting their lives. In some episodes, as in the Vermont one, we are validating children who are seldom validated. We believe that 'Postcards From Buster' does this in a very natural way -- and, as always, from the point of view of children."

Jeanne Hopkins, a spokeswoman for the show's producer, WGBH-TV of Boston, added, "We feel it's important that we not exclude kids because of what their family structure looks like." WGBH plans to broadcast the episode in March and offer it to other PBS stations.

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Like the grown-ups in most of the episodes, the lesbian mothers in the "Sugartime!" segment are mainly background. "The concern really was that there's a point where background becomes foreground," Mr. Godwin said. "No matter if the parents were intended to be background, with this specific item in this particular program they might simply be foreground because of press attention to it and parental attention to it."

The question is, does the episode violate the grant under which WGBH received federal funds? Mr. Godwin said, "The presence of a couple headed by two mothers would not be appropriate curricular purpose that PBS should provide."

The grant specifies the programs "should be designed to appeal to all of America's children by providing them with content and characters with which they can identify." In addition, the grant says, "Diversity will be incorporated into the fabric of the series to help children understand and respect differences and learn to live in a multicultural society."

Brigid Sullivan, vice president for children's programming at WGBH, has been producing children's shows for 20 years, including "Arthur," for many years the top-rated children's show. "This asked for a project on diversity to all of America's children," she said. "We took it seriously and thought that with 'Arthur,' the No. 1 show on television for kids for years, we had something to draw kids in. Buster is Arthur's best friend, the child of divorce, he has asthma. Children sympathize with him. We had a breakthrough format, this animated bunny with his camera getting live-action sequence. Not to present a make-believe world of diversity but a real world."

Explaining the goal of the show, Ms. Sullivan said: "We want to reflect all of America's children."

"This is not about their parents," she said.

Correction: January 29, 2005, Saturday An article in The Arts on Thursday about a decision by PBS against distributing an episode of "Postcards From Buster," a children's program, because it portrays children whose parents are a lesbian couple, referred incorrectly to another recent controversy over a children's television character, SpongeBob SquarePants. Dr. James C. Dobson, founder of the conservative Christian group Focus on the Family, said this month that SpongeBob's creator had allowed the character to be used in a "pro-homosexual video." He did not say the SpongeBob character itself was "pro-homosexual." (The creator of the video said it was intended to teach children about multiculturalism.)

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Correction: March 12, 2005, Saturday A front-page article on Feb. 17 about challenges faced by PBS referred imprecisely to events that preceded the organization's decision on Jan. 26 against distributing to its stations a children's program in which lesbian parents appeared. (The error also occurred in articles on Jan. 27 and Feb. 16.) While PBS officials discussed the program with Education Department officials before the decision, a letter from Education Secretary Margaret Spellings, denouncing the program, was received after the decision was made, PBS said.