Assessment in higher education has been impacted by generative artificial intelligence (GenAI), especially in the context of distance education. Academics and educators have raised concerns regarding academic integrity and authenticity as students use GenAI-generated information to complete assessments as it becomes more widely accessible. This qualitative study investigates the influence of GenAI on assessment in distance higher education within the framework of an open distance e-learning university in South Africa. The objectives of this study are to explore (i) why students use GenAI to complete assessments, (ii) investigate how markers evaluate and interpret AI-generated responses in student assessments, and (iii) explore the challenges lecturers experience when they design assessments that that aim to minimise the use of GenAI. The community of inquiry theory forms the basis of this study and notes the interdependence of social, teaching, and cognitive presences in online learning contexts. The findings within this study shows how GenAI influences these presences’ dynamics; and, in turn, students’ motivations for their uses of GenAI in assessments. The research instruments used were focus group discussions, WhatsApp interviews, and email semi-structured interviews to collect data from students, markers and lecturers to understand the challenges related to GenAI in assessment. The findings contribute to the ongoing discussions on academic integrity and assessment in the era of GenAI and have important theoretical and pedagogical implications for stakeholders in higher education institutions.