Student access to digital writing technology has become increasingly prominent across various school subjects and education levels. Promoting a techno-optimist approach to solving pedagogical challenges, access has predominantly been foregrounded as something that students are 'provided', that is, access is to be uptaken by human individuals. In this article, we trouble this notion through exploring the affective potentials of access to writing technology. Advocating relational thinking, access is understood to hold multiple potentials in students' writing practices. We focus on students' task-related writing on screens, in the school subjects L1 (Language and Literature) and Social Studies in lower secondary classrooms in Finland and Sweden. Drawing on video-data, the analysis shows how access holds the potential of becoming sticky, slippery, and smooth in students' writing, further engaging students and teachers in sociotechnical care work in classrooms.