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Cynthia Daily and her partner used a sperm donor to conceive a baby seven years ago, and they hoped that one day their son would get to know some of his half siblings — an extended family of sorts for modern times.

So Ms. Daily searched a Web-based registry for other children fathered by the same donor and helped to create an online group to track them. Over the years, she watched the number of children in her son’s group grow.

And grow.

Today there are 150 children, all conceived with sperm from one donor, in this group of half siblings, and more are on the way. “It’s wild when we see them all together — they all look alike,” said Ms. Daily, 48, a social worker in the Washington area who sometimes vacations with other families in her son’s group.

As more women choose to have babies on their own, and the number of children born through artificial insemination increases, outsize groups of donor siblings are starting to appear. While Ms. Daily’s group is among the largest, many others...