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The emails arrived by the dozens. Then the hundreds. Then the thousands.

Family and friends of Sarah Murnaghan had posted an online petition demanding that the 10-year-old, whose lungs were ravaged by cystic fibrosis, be given the same access as adults to organs from adult donors — and not be limited to organs from children.

Each time somebody signed it, Dr. John Roberts received another email.

“Children should be at the top of the list,” one said.

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“I don’t want Sarah to die,” said another.

More than 372,000 people signed the petition on behalf of the girl from Newtown Square, Pa. Roberts’ inbox crashed after about 48,000 emails.

Roberts, chief of transplantation at the University of California, San Francisco, and president of the United Network for Organ Sharing, the nonprofit that oversees the national transplant system for the federal government, said the campaign was an eye-opener.

“Maybe the populace wants children to have more access than we’re giving them,” he said.

Last week a federal judge ignited a national debate by ordering that Sarah — as well as Javier Acosta, an 11-year-old boy with cystic fibrosis who is also waiting for lungs at Children’s Hospital of Philadelphia — be allowed to compete on an equal basis with adults for lungs from adult donors.

Sarah underwent a transplant Wednesday, receiving lungs from an adult, according to a family spokeswoman. “Her doctors are very pleased with both her progress during the procedure and her prognosis for recovery,” the family said in a statement.

On Facebook, Sarah’s mother, Janet, praised the anonymous donor.

“Please pray for Sarah’s donor, her HERO, who has given her the gift of life,” she wrote.

Sarah’s case may be resolved, but the bigger issues raised by her transplant are not.

Federal transplant officials took offense that a court interfered with a carefully calibrated organ-allocation system. This week, the executive committee of the national organ network rejected an emergency rule that would have given the same advantage to all children in need of lungs. Instead, officials agreed to allow hospitals to petition a national board in individual cases while they study the lung-allocation rules over the next year.

Nobody wants to deny transplants to children. In fact, minors generally receive preferential status for organs.

But allocation of lungs is particularly complicated.

Before 2005, all patients regardless of age waited in line for lungs on a first-come, first-served basis. Adults and children competed equally for all lungs — though adult organs usually wound up going to adults because they were too big for most children.

Today, children younger than 12 are first in line for lungs from donors their own age. They are second in line for lungs from adolescent donors, ages 12 to 17, behind members of that age group. They can get adult lungs only if no adult can use the organs, which is rare.

Although adolescents 12 to 17 are given preference for lungs from donors in their age group, they also are eligible for adult lungs and wait with adult patients on a list that ranks everyone using an algorithm taking into account both the severity of their condition and the likelihood that a transplant will be successful.

The rules are based on statistical models built on years of data that take into account death rates among people waiting for lungs and survival rates after transplantation.

The rationale for the two-tier system, in addition to organ-size considerations, is that the criteria used to rank adults on the list often don’t work for children, who generally suffer from a different set of diseases.

The experts who made the rules saw no good way around an age cutoff. They chose 12.

Lung transplants for children are rare. Of 1,754 operations last year in the United States, just 32 were for patients younger than 18, according to the organ network. Fourteen children died waiting.

As of last week, 70 minors were waiting for lungs, along with 1,589 adults. Last year, 1,722 adults were given lung transplants, and an additional 210 died before they could receive an organ.

Sarah received only a portion of the adult donor lungs, according to the family spokeswoman.

Such an operation, known as a deceased donor lobar transplant, had not been performed for a child in the United States in several years, transplant officials said.

Lawyers for the Murnaghan family argued that the current policy is tantamount to age discrimination. They presented statistics to the court showing that among people waiting for lungs, children die at a higher rate than adults.

At the heart of the debate over how to allocate organs is a grim fact. Giving an organ to one person denies somebody else, raising a variety of painful ethical questions.

“Should all children be transplanted first?” Roberts said. “Then you run into another question. Who is a child? Should a 17-year-old have more access than a 19-year-old?”

“Society wants us to give priority to kids,” he said. “But is it fair that they have more access than a young adult with three kids who is the primary breadwinner?”

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