Most children growing up in contemporary homes in post-industrial countries use digital media as part of everyday literacy activities, such as to connect with distant family and friends, watch their favourite programmes, play games and find information. However, conceptualizations of the Home Literacy Environment (HLE) have not yet adapted to the implications of these comparatively new practices for young children's knowledge about literacy or the ways in which they negotiate affectively intense relationships in digital networks. Furthermore, the digital activity of very young children aged 0-3 years and the diversity of print and digital technologies they use remain under-researched. Reporting on detailed case studies of a two-year-old boy and a one-year-old girl in England, which formed part of an EU-wide qualitative study of 0-3-year-olds' digital literacy practices at home, we problematise the relevance of conventional definitions of the HLE for contemporary homes. Building on nascent research in this field, we argue for the need to reconceptualise the HLE as a digitally networked space, with porous boundaries that enable the very youngest children to negotiate affectively intense relationships and express meaning across diverse modes and media as they connect with distant others in a digitally mediated world.