The most detailed work (that I know of) dealing with the concept of song ownership as a social asset (particularly where some singers might have much smaller repertoires than others) in a community is Ginette Dunn's The Fellowship of Song: Popular Singing Traditions in East Suffolk (1980, and long out of print, unfortunately) -an important book that ought to be better-known.

The same principle applies, to a greater or lesser extent, in any discrete and established community; in families, for example. A grandmother may "give" to a grandchild, perhaps, a song that her son or daughter might have coveted (and had learned, but was not allowed to sing in company). The relationship between Belle Stewart and her daughters is full of questions of that sort, and Jeannie Robertson and her daughter Lizzie Higgins had clear (though not always comfortable) lines of demarcation between their respective repertoires.

I'm not saying that it's the way things ought to be; just that, historically, it's the way that things have been. In an established community it isn't all that hard to know where the various boundaries are drawn (though disputes will occur); in an "ad-hoc" community like a folk club or session, it can be a positive minefield, particularly where the competing performers don't know each other. We are territorial animals, after all, and though we are often able to share quite comfortably, there will inevitably be times when we bridle at a perceived intrusion into personal space.