Context. Debris disc analysis and modelling provide crucial information about the structure and the processes at play in extrasolar planetary systems. In binary systems, this issue is more complex because the disc should also respond to the companion star’s perturbations. Aims. We explore the dynamical evolution of a collisionally active debris disc for different initial parent body populations, diverse binary configurations, and optical depths. We focus on the radial extent and size distribution of the disc in a stationary state. Methods. We numerically followed the evolution of 105 massless small grains, initially produced from a circumprimary disc of parent bodies following a size distribution in dN?∝?s-3.5ds . Grains were submitted to both stars’ gravity and radiation pressure. In addition, particles were assigned an empirically derived collisional lifetime. Results. For all the binary configurations, the disc extends far beyond the critical semi-major axis acrit for orbital stability. This is due to the steady production of small grains, placed by radiation pressure on eccentric orbits reaching beyond acrit. The amount of matter beyond acrit depends on the balance between collisional production and dynamical removal rates: it increases for more massive discs, as well as for eccentric binaries. Another important effect is that, in the dynamically stable region, the disc is depleted from its smallest grains. Both results could lead to observable signatures. Conclusions. We have shown that a companion star can never fully truncate a collisionally active disc. For eccentric companions, grains in the unstable regions can contribute significantly to the thermal emission in the mid-IR. Discs with sharp outer edges, especially bright ones such as HR4796A, are probably shaped by other mechanisms.
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