Purpose - The purpose of this paper is to analyze this phenomenon and identify its determinants using data from Brazilian higher education institutions. Design/methodology/approach - Based on a data set comprehending 2,230 university students from 70 different institutions across the country, the authors develop five Probit models to assess impacts related to individual traits and systemic conditions on five dependent dimensions: entrepreneurial activity, potential entrepreneurs, high-impact entrepreneurship, serial entrepreneurship and innovation-driven entrepreneurship. Findings - The lack of significance in many of the variables included in estimations suggests that student entrepreneurship seems to be a rather random phenomenon in Brazil. Research limitations/implications - Findings pose challenges for student entrepreneurship, as targets for intervention are not clear. Originality/value - Over the past decades, universities have been receiving an increasing demand to go beyond their role of producing science and technology to explore its knowledge potential to produce novel commercial applications. However, while there is a growing interest in ways to foster scientific academic entrepreneurship, universities also serve as a positive environment for student entrepreneurship training, knowledge sharing, testing ideas and learning. So far, the importance of student entrepreneurship has received far less attention than it likely deserves.