There is a strong rationale for people seeking asylum and refugees given temporary protection to be key beneficiaries of Australian higher education equity practices. However, despite the extreme precarity they face, this group remains among the most educationally disadvantaged populations in Australia. Here, we use critical discourse analysis to examine the publicly available statements of 38 Australian universities to identify discursive representations of equity practices and connections, with our analytic gaze focused through the lens of people seeking asylum. Using a three-part analytic heuristic examining 'statements', 'practices' and 'connections', we offer a critical discourse analysis of how each public university expresses its commitment to the equity agenda in powerful stakeholder-facing documents--such as annual reports, strategic plans and media releases--and we compare this analysis against institutional stated practices with regard to people seeking asylum. In identifying misalignments between equity statements and stated practices, we suggest that institutional equity narratives articulate 'imagined worlds', in which all marginalised groups can access higher education. We argue that now is the time to move beyond these 'imagined worlds', to enact stated commitments to universal education, by instituting real and effective practices to facilitate equitable access to Australian higher education for people seeking asylum.