When postgraduate researchers' interests lie outside the body(ies) of knowledge with which their supervisors are familiar, different supervisory approaches are called for. In such situations, questions concerning the appropriateness of traditional models arise, which almost invariably involve a budding candidate's relationship with a knowing-established researcher/supervisor. Supervisory relationships involving creative practice-led research in particular confront significant challenges by new and emerging themes, questions, processes and practices. My lack of disciplinary knowledge regarding two PhD candidates' projects led me some years ago to question the effects of this lack and to search for effective ways of dealing with it. A subsequent commitment to different modes of candidate/supervisor collaborations was based on three assumptions: One, a supervisor is not, in the first instance, a conveyor or purveyor of knowledge. Two, postgraduate researchers already have substantial and refined pockets of relevant knowledge to draw on. Three, and very importantly, they are able to activate networks of distributed knowledge, often outside of the University. The argument presented in this article draws theoretically on Jacques Rancière and Hannah Arendt's ideas of pedagogy and public space, as well as notions of cosmopolitics (Cheah & Robbins), mode 2 knowledge (Gibbons et al.) and not-knowing in Art & Design (Jonas). Reflections on my experiences of supervising PhD and Master of Art & Design candidates, together with ideas offered by contributors to a book I have recently edited, will locate moments of choice and the emergence of the unforeseeable, of vigilance towards singular events as much as collective understanding.