A North Jersey toddler received a kidney from a San Francisco woman, and her father donated one of his to a man in Los Angeles on Friday as Hackensack University Medical Center participated in a continent-spanning chain of kidney transplants.

Payton Dimick, a bubbly 22-month-old girl, was the third patient in a chain of five transplants that began Thursday at UCLA Medical Center and is to end next Thursday at the University of California, San Francisco.

Ten operations, five airline shipments, and four hospitals in three states — California, New Jersey and Nevada — are involved in the carefully orchestrated plan. It included a lights-and-sirens drive up the New Jersey Turnpike for one kidney, and a chartered jet for another out of Teterboro.

The unrelated donations, organized through the National Kidney Registry, aim to shorten the waiting period for those in need through a computerized matching system that combs through a pool of willing donors nationwide. Often, a patient in need of a transplant has a willing but incompatible donor. This allows those donors to “pay it forward” by donating to a compatible stranger, so their loved one or friend can benefit in turn from a similar donation.

“One person’s donation has a domino effect,” said Barbara Turci, assistant clinical director at the New Jersey Organ and Tissue Sharing Network, which coordinated the New Jersey logistics.

By scanning a national pool, better matches are possible. And by tapping into donations from living donors, the registry vastly expands the number of transplant operations that can be done. The registry was started by a business executive whose daughter needed a transplant and had a hard time finding a match among several willing donors.

“It turns out that if you let yourself do more extensive swaps you can do better matches, and you can find matches for more people,” said Dr. Michael Shapiro, chief of organ transplantation at Hackensack.

For transplant recipients, the less time spent on dialysis or on a waiting list, the better. They are healthier when they undergo surgery and have better long-term prospects. For donors, the remaining kidney takes over the job that both once did.

Payton and her father Jason Dimick, a 31-year-old police detective in Mountain Lakes, joined the registry last summer and learned a month ago that their chain had been put together.

Payton was born with “bad kidneys,” her father said. She received a transplant in May from a deceased donor, but her body rejected it. As a result, she developed antibodies that rule out many potential donors.

Every night, the 23-pound Rockaway girl has had to undergo dialysis as she sleeps. Most of her nutrition has been provided through a feeding tube. The family keeps hand sanitizer at the ready, and keeps their house, especially her room, as clean as possible — particularly before the operation, when her immune system was suppressed.

Although they would have willingly given their daughter a kidney, “my husband and I aren’t matches,” said Stacy Dimick on Thursday afternoon. “We tested nine of our friends and family who offered to donate, and none of them were matches, either.”

As she spoke, Payton toddled happily around her toy kitchen, unaware of life-changing events that had already been set in motion.

Across the country, at the UCLA Medical Center, a kidney was recovered Thursday morning from a woman whose longtime friend had received a transplant in November. It was flown to San Francisco, where it was given to a 30-something father of two whose wife was incompatible with him as a donor.

On Thursday afternoon, his wife donated one of her kidneys for Payton.

As Jason, Payton, and Stacy set off early Friday morning to Hackensack, Payton’s future kidney was on the red-eye from San Francisco to Newark. Ruben Lambert, an organ recovery specialist for the New Jersey Sharing Network, was on his way to Newark Airport to pick it up. And Shapiro, at his office in Hackensack, was on his computer to monitor the flight’s progress. It was 20 minutes behind schedule.

A baggage agent handed Lambert the package — marked “Donated Human Organ/Tissue for Transplant, Left Kidney, Handle with Care” — at 7:10 a.m. With his siren wailing, Lambert hit 70 miles an hour on the 30-minute drive to Hackensack.

Shapiro, in scrubs, took the hand-off at the portico of the medical center at 7:39 a.m.

In the operating room, the anesthesiologist put Payton to sleep.

Shapiro started the transplant as his colleague, Dr. Ravi Munver, began surgery to remove Jason’s left kidney. Lambert, a general surgeon in Cuba before he immigrated to the United States in 1993, scrubbed and joined Munver.

His job was to prepare Jason’s kidney for shipment and transplant. Using a special solution, he drained it of blood. He trimmed the fat away and made sure the blood vessels were clear and visible. Then he sealed it in a plastic bag with a preservative liquid and sterile ice chips.

The bag was placed in a hard plastic jar, then in another plastic bag — three sterile layers of protection, all carefully labeled.

Lambert put this in a cooler, and then put the cooler in a cardboard box. Changing back into street clothes, he drove the package to Teterboro Airport, where a chartered jet waited. The five-hour flight to Los Angeles began at 11:30 a.m.

Back at the hospital, the surgeons finished up their operations.

“It could not have gone better,” Shapiro said of both. Payton is to be in the pediatric intensive-care unit for a few days. Her father should be able to go home in three or four days.

Stacy Dimick said Friday afternoon that Jason was doing well, but felt “really tired.” Payton was still asleep, and will be sedated for a few days.

The adult kidney in Payton’s tiny frame is a “snug fit,” Shapiro said. But “it turned pink right away,” as blood began to circulate through its vessels. And most importantly, “It’s peeing.”

E-mail: washburn@northjersey.co