Young children's engagements with digital technologies form part of their emergent everyday literacy practices. The study reported here derives from the pan-European study 'A Day in the Digital Lives of Children aged 0-3'. The methodology was centred on the videoing of an entire day's experiences of a child aged under 3, together with a reflective interview with the parents and inventories related to digital access, skills and activities of the child. In this paper, we look at three children in Spain, Sweden and England, respectively. We examine our data through three prisms. (1) Spatio-temporal: We consider the children's engagements in terms of their appropriation of space, in relationships with others in the home and the intimate geographies of young children's digital literacies. (2) Parental discourse: We use the tensions and contradictions for families framework to examine the selection and monitoring of digital literacies. (3) Practice: Drawing on the first two prisms, we zoom into how children engage with tablet devices and television. Our research demonstrates richness, diversity and agency in these young children's practices with technologies. We propose the concept of living-room assemblage as an analytical metaphor to understand the macrohabitats of young children's digital literacies and practices, which emerge as multi-layered, creative and co-occurring with other family activities. Our analysis also explores the challenges presented to parents and the ways in which they navigate tensions and contradictions in their media and digital environments, which are condensed in family practices and discourses around tablets and television.