The BPI in Paris offers a particularly wide range of material to all readers, with no need for registration. How do readers use the library, both on and off site? While recent indicators point to a fall in on-site reader numbers and a drop in use of print holdings, there is no evidence that readers prefer accessing on-line material rather than visiting the library premises. Far from creating competition between real and virtual visitors, digital materials reflect a complex set of ongoing shifts in patterns of use, both on- and off-site. This article examines how users see their relationship to the library and its premises, holdings and services, and questions the usual dichotomy between on-site and off-site library use, "inside" vs. "outside", reading the relationship rather in terms of a new dynamic of proximity vs. Distance.