  How does the cavity size in circumbinary discs depend on disc and binary
properties? We investigate by simulating disc cavities carved by binary
companions using smoothed particle hydrodynamics (SPH). We find that a cavity
is quickly opened on the dynamical time, while the cavity size is set on the
viscous time. In agreement with previous findings, we find long term cavity
sizes of 2-5 times the binary semi-major axis, increasing with eccentricity and
decreasing with disc aspect ratio. When considering binaries inclined with
respect to the disc we find three regimes: i) discs that evolve towards a
coplanar orbit have a large cavity, slightly smaller than that of an initially
coplanar disc; ii) discs that evolve towards a polar orbit by breaking have a
small cavity, equal in size to that of an initially polar disc; iii) discs that
evolve towards a polar orbit via warping have an intermediate-sized cavity. We
find typical gas depletions inside the cavity of $\gtrsim 2$ orders of
magnitude in surface density.
