Here is an example of how much work can be spent chasing down a relative that turns out to be unrelated.
While browsing through census records for information about my Donnelly (and related) family, I found a Mary Lang living with John and Catherine Gorman Murphy. Catherine is a granddaughter of my great great great grandparents, Patrick and Nancy Larkin Donley. Mary Lang is described as a niece. So I embarked on a search for the relationship between the Langs and the Gorman or Murphy family.
A search of historic newspapers revealed that Mary Lang was also a niece of the Murphys' next door neighbors, Alexander and Elizabeth Creighton, and that Mary was from Minnesota or Wisconsin. I'll skip all of the convoluted search details, but it included searches through newspapers, census records and cemetery records. After assembling a tree of over 100 people, I was finally able to find a distant link between families.
Mary G Lang was the daughter of Nicholas Lang and Mary Ann Dinnenny, born in 1885, probably in Waddington, New York. In 1890, Mrs. Lang moved the family to Felton, Minnesota. I have not found any news of Nicholas, so am not sure whether he died or whether they split up. Living in Felton was Christopher Dinnenny and family, whom I believe to be Mary Ann's brother, and probably the reason for moving there. Mary Ann married Albert Fox in 1895. In 1908, Mary G returned to Waddington and spent the next four years with her aunt, Elizabeth Dinnenny Creighton. I'm not sure why she was living next door at the Murphys' in 1910. Perhaps she was renting a room at their house. I'm guessing she was described as a niece of the Murphys because the true relationship was too complicated.
Mrs. Catherine Gorman Murphy's much younger first cousin on her father's side, John Augustus Gorman, was married to Anna Fay. Anna's first cousin on her father's side, James Fay, was married to Mary Creighton, daughter of Mary Lang's aunt Elizabeth Dinnenny Creighton. Said another way, Mary Lang's first cousin's husband's first cousin's husband's first cousin is Mrs. Murphy. Or Mrs. Murphy is the first cousin of the husband of the first cousin of the husband of Mary Lang's first cousin. Mrs. Murphy is not Mary Lang's aunt, but the term was used to describe a generation difference in age and some not-simple relationship.
Even though all this work did not lead to Mary Lang being related, it did allow me to answer another difficult question in my family tree. Bridget Donley and Thomas Gorman's daughters, Catherine and Mary Ann, both married Murphys, John and Michael, respectively. I was able to establish that John and Michael Murphy were brothers, sons of Elizabeth Stafford and Moses Murphy. While many of the individuals in this research are not related to me, I have added them to my family tree in order to show the string of relationships between the Murphys and their "niece", Mary Lang.