This throws a monkey wrench into simply copying old papers or encyclopedia chunks. Be very clear about what can be collaborative and what cannot be collaborative. For instance, if students are welcome to work in groups on an experiment, or to find source materials, or to brainstorm, but must compose in isolation, but may then edit and proofread in groups or with tutors or some such combination, state the acceptable mix very explicitly. After all, in some classes collaborative learning is required, while in others, it is prohibited. Keep in mind that most of us talk to our colleagues about writing projects we are working on, ask for reaction, and take pointers about sources we might have overlooked.
Some departments even have editors available to do final mark-up of manuscripts.
Therefore, we need to help students be productive writers in the modes we have found useful while at the same time being clear about boundaries we require for their work. And in some disciplines, part of the ethic is co-authorship. Students need to hear explicitly, from each teacher in each course, what the boundaries are. In general, I think it is very important for faculty to define plagiarism in the context of their particular course, to do so in writing, and to do so at some length. Genuine dishonesty is always repugnant.