Evidence is accumulating from Australia and elsewhere that border-control policies aimed at preventing arrival, when they fail to deter asylum seekers and other unwanted migrants from attempting illegalised1crossings, significantly increase the risk of fatalities. However, the chains of responsibility for border-related deaths are difficult to discern because the visible face of offshore border control is underpinned by a virtual border that is seldom brought into view. While the exercise of sovereignty is readily apparent in the spectacle of direct encounters between border authorities and border transgressors, the virtual border is enacted through electronic information exchange and largely unseen human operators. This bifurcation of the border function is typical of modes of governance in late modernity described by Haggerty and Ericson as ‘surveillant assemblages’ and referred to by O’Malley as ‘simulated enforcement’. In this article I identify the visible and virtual aspects of Australian offshore border controls as parts of a surveillant assemblage, and argue that perceiving these elements as a single border-enforcement system is essential for saving lives and debating new ways of conceiving sovereignty in a globalising world.