PurposeUniversities claim to provide many benefits to their context. What remains less clear is what is meant by context. Whatever it is, context is fundamental to decision-making. Understanding what context means is crucial to understanding leadership in higher education.Design/methodology/approachTheoretically informed by Eacott's relational approach, this study is based on interview data from a purposive sample of ten English vice-chancellors and nine Canadian university presidents. Transcripts were analysed for the assumptions participants held regarding the work of universities and how that played out in practice.FindingsContext is not an external variable engaged with or acted upon. It is not separate to leadership and the work of universities but is constitutive of and emergent from activities. There is no single definition of context, and this has major implications for university activities.Research limitations/implicationsContext(s) is based on assumptions. Making explicit the assumptions of participants, without pre-defining them, is a key task of research on leadership in higher education.Practical implicationsLeaders need to explicitly articulate their assumptions regarding the work of universities. Assessment should be based on the coherence between the espoused position and activities undertaken.Originality/valueThrough the emerging resources of relational scholarship, this paper demonstrates how context is constitutive of and emergent from the activities of universities. More than novel vocabulary, the paper makes a fundamental point about the generative nature of context. De-centring entities (e.g. university, leader, context) and focusing on relations our approach provide a path forward by encouraging the articulation of intended purpose(s) and perspective on the work of universities.