Many families are grappling with similar questions as a family tree today is beginning to look more like a tangled forest. Genealogists have long defined familial relations along bloodlines or marriage. But as the composition of families changes, so too has the notion of who gets a branch on the family tree.

Some families now organize their family tree into two separate histories: genetic and emotional. Some schools, where charting family history has traditionally been a classroom project, are now skipping the exercise altogether…

Rob Okun, a 61-year-old magazine editor from Massachusetts, agreed to donate his sperm to a lesbian couple 16 years ago. Mr. Okun already had two biological children with a longtime female partner and two stepchildren with his current wife. He wanted no role in parenting the children born with his donated sperm, but did want them to know who he was.

The couple, Patricia Kogut and Lynne Dahlborg, agreed, and Ms. Kogut gave birth to Lucyna and Nathaniel. Ms. Dahlborg then adopted both children.

“There is the family tree and there is the day-to-day structure of the family,” Ms. Kogut said.