BOSTON — Kianni Arroyo clasps 8-year-old Sophia’s hands tightly as they spin around, giggling like mad. It’s late afternoon, and there are hot dogs on the grill, bubble wands on the lawn, balls flying through the air.

The midsummer reunion in a suburb west of the city looks like any other, but these family ties can’t be described with standard labels. Instead, Arroyo, a 21-year-old waitress from Orlando, is here to meet “DNA-in-laws,” various “sister-moms” and especially people like Sophia, a cherished “donor-sibling.”

Sophia and Arroyo were both conceived with sperm from Donor No. 2757, a best-seller. Over the years, Donor No. 2757 sired at least 29 girls and 16 boys, now ages 1 to 21, living in eight states and four countries. Arroyo is on a quest to meet them all, chronicling her journey on Instagram. She has to use an Excel spreadsheet to keep them all straight.

“We have a connection. It’s hard to explain, but it’s there,” said Arroyo, an only child who is both comforted and “weirded out” by her ever-expanding family tree.

Thanks to mail-away DNA tests and a proliferation of online registries, people conceived with donated sperm and eggs are increasingly connecting with their genetic relatives, forming a growing community with complex relationships and unique concerns about the U.S. fertility industry. Like Arroyo, many have discovered dozens of donor siblings, with one group approaching 200 members — enormous genetic families without precedent in modern society.

Because most donations are anonymous, the resulting children often find it almost impossible to obtain crucial information. Medical journals have documented cases in which clusters of offspring have found each other while seeking treatment for the same genetic disease.

While Britain, Norway, China and other countries have passed laws limiting the number of children conceived per donor, the United States relies on voluntary guidelines. That has raised fears that the offspring of prolific donors could meet and fall in love without knowing they were closely related, putting their children at risk of genetic disorders.

Now the donor-conceived community is starting to demand more government regulation — so far with mixed results. Earlier this year, Washington and Vermont became the first states to require clinics to collect donors’ medical histories and to disclose that information to any resulting children. Similar bills have been introduced in California and Rhode Island.

But last month, the Food and Drug Administration rejected a petition from a donor offspring group that sought to limit the number of births per donor, mandate reporting of donor-conceived births and require donors to provide post-conception medical updates. Peter Marks, director of the FDA’s Center for Biologics Evaluation and Research, wrote that such oversight exceeds the FDA’s mission, which is limited to screening donors for communicable diseases.

Sean Tipton, a spokesman for the American Society for Reproductive Medicine, which represents most of the nation’s fertility clinics, said such proposals would have infringed on the right to privacy and to procreate, giving government “control over who has children with whom.”

“We think these decisions are best made by the families, not by activists and certainly not by the government,” Tipton said.

The lack of federal action has infuriated members of donor families such as Wendy Kramer, a Colorado woman who penned the FDA petition.

“There is no government agency that wants to step in to regulate or oversee the business of creating human beings,” said Kramer, whose son, Ryan, 28, has so far discovered 16 half-siblings conceived with sperm from the same donor. “As wonderful as the connections are, there is an underbelly. It has really revealed how this lack of regulation has had ramifications for real families.”

Donor Sibling Registry

Eighteen years ago, Kramer and Ryan founded what has since become the largest online site for the donor-conceived, the Donor Sibling Registry, or DSR. In simplest terms, the DSR is a matching site. People type in their donor number — an anonymous code assigned by the fertility clinic — and connect with others born from sperm or eggs from the same donor. It’s all voluntary, and contact is achieved through mutual consent.

Today, the DSR has more than 60,000 members and has helped connect about 16,000 offspring with their half-siblings or donors. As the site grows, so does the potential for new connections. Ryan has discovered five “new” sisters in just the past four months.

Jennifer Moore, a 55-year-old graphic designer from Loveland, Colo., has two boys conceived with donor sperm. Through the DSR, they have connected with triplet half-siblings in another part of the country.

The boys call one another “bro” and are all very athletic. They are also all “into crazy socks and hats and crazy fashion sense,” Moore said, adding: “As a parent, it has been a bizarre experience having that many clones of your children appear before your eyes.”

Their parents try to get all the half-siblings together at least once a year, Moore said. Though her boys have a father, her ex-husband, she wants them to know more about their background and not wonder why they might look or act different from their parents.

“Foundationally, everyone has a right to know where they came from,” she said.

While a growing number of the donor-conceived are seeking to connect with half-siblings, it can be harder to find the donors, who may not want to be found. But internet sleuthing and the widespread availability of genetic testing is eroding the guarantee of anonymity they once enjoyed. So far, Moore’s donor has proved elusive, but she has been in contact with several of her sons’ genetic cousins, discovered on an ancestry site.

One of the most important revelations of the DSR has been to confirm the existence of prolific sperm donors — real-life versions of the Vince Vaughn character in the movie “The Delivery Man” who learns that he fathered 533 children through his donations.

Many countries set strict limits on the number of offspring a donor can sire. In Britain, it’s up to 10 families; in Netherlands, 25; in Taiwan, just one. But no such laws exist in the United States, where the American Society of Reproductive Medicine recommends limiting live births per donor to 25 per 800,000 population — about the size of San Francisco or Charlotte. In a nation of 326 million people, that works out to a staggering 10,175 possible children per donor.

Concerns about prolific donors are not theoretical. Kramer and other parents tell their kids to memorize their sperm or egg bank name and donor number, and to share that information with potential dates. She knows of a camp counselor who stumbled onto a half-brother while talking with a camper. In another case, two women searching for roommates at Tulane University discovered they were half-sisters.

Finding family

Kianni Arroyo had to work harder to meet her genetic family. The first person she found was her biological father.

Donor No. 2757 stands 5-foot-10 and weighs 185 pounds. He has hazel-green eyes, wavy brown hair and is descended from German, Irish and Native American stock. In his profile, he’s described as a photographer with a bachelor’s degree who likes biking, surfing and writing. He donated his sperm to pay off college student loans.

The women who chose Donor No. 2757 did so for various reasons. Arroyo’s mom liked his looks and his artistic background. Another woman, who would later give birth to Zac LaRocca-Stravalle, now 19, liked that he could trace his lineage to a brave military officer whose exploits were documented by historians. Rebecca, the mother of Sophia and twin Ava, thought “he seemed like someone I’d date.” (Rebecca asked that she and the twins be identified only by their first names to protect their privacy.)

Arroyo went searching for her donor’s identity in her teens and met a person active in the donor-offspring community who had somehow gotten that confidential information. She friended her donor on Facebook and contacted him shortly before her 18th birthday. They met when he was in Orlando on a business trip. She drove to his hotel and looked for a man who looked like her.

“When I found him, I didn’t know whether to hug him or shake his hand or not touch him at all. It was really awkward,” Arroyo recalled. “But then he kind of opened his arms into a hug and accepted me. It was kind of relieving.”

Donor No. 2757 told her he was still working as a photographer, that he was single and that he had no children of his own. Through Arroyo, he declined to be interviewed or identified, citing privacy concerns.

About a year later, the donor connected Arroyo with her first half-sibling: JoAnna Alaia, 20, of Tampa, who works in business administration. She’s a twin, but her twin was not interested in meeting with Arroyo. So the two women drove all night and met with Donor No. 2757 the next day in his hometown.

Since then, their sibling group has mushroomed. Arroyo has discovered seven half-siblings in Florida and seven more in New York, five in Massachusetts and four in Georgia. Because American sperm is sold widely overseas, she has also found half-siblings in Australia, New Zealand and Canada.

So far, Arroyo is the oldest, but not by much. There are 10 other 20-somethings. Then there seems to be a decade-long gap before another batch of half-siblings arrived, children now in elementary school.

This summer, Arroyo’s vacation plans revolved around meeting her donor siblings. She, Sophia and Ava spent a few days on Cape Cod with a 9-year-old half-sister from New York who has her donor number tattooed on her wrist. Then they hosted a cookout in the Boston area for the Massachusetts-based families.

Five of Arroyo’s half-siblings were at the reunion: Sophia and Ava, LaRocca-Stravalle and another set of twins, Addeline and Vivianna Juliani, age 8. Everyone noted the family resemblance: The laid-back, sporty kids all had wide smiles and prominent dimples on their right cheeks.

Kristen Juliani, one of the twins’ two mothers, recounted how a sperm bank sales person had recommended Donor No. 2757 as a “model” donor. She was not thrilled to learn that her donor was so popular.

“I don’t feel great about it,” she said. “There should be a cap on sales.”

Arroyo has mixed feelings, too. While every visit with her half-siblings has been a blast, she finds it “worrying” that sperm banks permit so many children to be born from a single donor.

“Every time I find a new sibling,” she said, “I get anxiety and think to myself: When is it going to end?”

A few days before she left the reunion, Arroyo got a message from yet another half-sister. Rylie Hager, 19, is a sophomore studying sociology at Temple University in Philadelphia. Arroyo invited her to join a group of half-siblings who planned to meet Donor No. 2757 in mid-August. The first night, they went bowling, and Hager noted that three of the girls were wearing the same outfit: gray tank tops and shorts.

“It’s all really crazy,” she said. “These people are strangers, but because I’m related to them, they have all kind of accepted me.”

Hager said when she first found out about the size of her group of half-siblings, she sent an alarmed text to her mom. “Is that exciting to you, or terrifying?” her mom asked.

Hager replied: “Both.”