A baby girl has received a liver transplant less than a month after hundreds of donation offers poured in.

Nine-month-old Delfina Budziak, from Vaughan, Ont., was diagnosed with biliary atresia two months into her short life.

Biliary atresia is a rare, life-threatening disease that begins in early infancy, according to the Canadian Liver Foundation. The bile duct that leads from the liver to the intestine becomes damaged, preventing bile from leaving the liver. This can lead to a build-up of bile in the liver and eventually liver failure. The cause of the disease is not known.

Since her diagnosis, Delfina has undergone several procedures and suffered infections of the liver. In late April, she had such a bad infection that she was hospitalized at Toronto’s Hospital for Sick Children. She's had to stay at the hospital since the infection.

At the end of May, Delfina's parents went public with an emotional plea for a liver donation. At the time, her parents said many of her family members had been tested to be donors, but none were identified as viable.

Her mother has the same blood type, but she was suffering from liver damage at the time and was told she could not donate.

Baby gets part of mother's liver

The baby girl's parents took to social and traditional media to ask for help. In a statement on Friday, the family said more than 1,000 people responded to their plea. Many of those who offered a portion of their liver also signed up to help anyone else in need.

A few days after the parents' plea, Delfina’s parents were told that the girl’s mother could undergo a procedure in hopes of becoming a viable donor. At the time, it was not known how long the procedure would take, so the parents continued their search for another donor.

Earlier this week, it was determined that the mother had recovered enough to be a donor for her daughter. On Thursday, both Delfina and her mother, Betsy, underwent surgery, and both are recovering well.

In the statement sent Friday, the family said they were "extraordinarily grateful" for all the offers they received.

"We can’t thank people enough. Over 1,000 strangers stepped up to say they’d be willing to save our daughter," Delfina’s father Peter said in the statement.

The family said they continue to encourage people to sign up for the living donor program and help others like their little girl.

Infant needs organ donor