Paul,
In the 1920 U.S. census, my five-month-old grandmother and her twin brother were "boarders" at a widow's farm. There were other children boarding there, as well as the woman's own "son" (I later learned he wasn't really her son: his father just paid her better to keep him). I wrote to the local family history society and learned that this woman took in unmarried women and unwanted babies and children.
At the same time, my grandmother's three-year-old sister was listed as a "boarder" in the home of her aunt, uncle and cousins, and they had a different surname. That family ended up raising my great-aunt.
So I've seen both situations. ; )
And I can't find either of my grandmother's parents in the 1920 U.S. census! It drives me crazy!
Regards,
Josephine