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“People’s primary concern is having a healthy, happy baby, and the safety of the mother,” he said.

Because donors remain anonymous, the service provides an easy and creative way to make the parents’ difficult selection a more “humane process.” Staff members carefully choose two or three celebrities who resemble a donor most closely, which Mr. Brown calls more of an “art than science.”

Because of anonymity, he said, “this was the best way we came up with to show what the donor actually looks like.”

And that is exactly the problem, said Elizabeth Marquardt, director of the Center for Marriage and Families at the Institute for American Values. She said that although the Donor Look-a-Like service is purely a “marketing strategy,” it wouldn’t be necessary if it weren’t for the clinic’s assurance of anonymity to the donors.

The Commission on Parenthood’s Future said in a report released this spring that an estimated 30,000 to 60,000 children a year are born as a result of sperm donation, although an accurate number cannot be determined because the industry is not required to report statistics.

The report, titled “My Daddy’s Name Is Donor,” studied 485 adults ages 18 to 45 who were conceived through sperm donation. The study shows that two-thirds of “donor offspring” believe they should know more information about their donor parent.

The issue also is reflected in popular culture. “The Kids Are All Right,” an independent film released this summer, centers on a lesbian couple whose children find out about their biological father, who then tries to become part of the family.

Britain, Sweden, Norway, the Netherlands and Switzerland are among countries that have banned anonymous donation of sperm and eggs. Parts of Australia and New Zealand have done the same.

“Pretending the donor doesn’t exist doesn’t make life more simple to the child; it just makes it more painful,” Ms. Marquardt said.

Ms. Kramer agrees. As a mother of a child conceived by sperm donation, she said, donor anonymity makes it difficult to receive medical information.

“Do you care if your donor looks like Ben Affleck if your child has a fatal heart condition?” she said. “It’s a business and it’s all about making money, hence the celebrity look-alike. Instead, they should be asking, ‘How can we better serve the needs of the children being born? How can we be more accountable? How can we share medical information with families?’”

The goal of Donor Sibling Registry is to educate parents about sperm donation and to update and share medical information, she said.

“There are really serious medical and genetic issues that arrive from creating so many [children] from one man’s sperm,” she said.