We present a probabilistic model of the dust mass, flux and fluence which will be collected by the ROSETTA probe while orbiting around comet 46P/Wirtanen. The dust environment of the target comet is simulated according to the most recent data available in the literature. Best fits of the DIDSY–GIOTTO data collected during the fly–by of comet 1P/Halley have shown that the probabilistic properties of dust ejection from the inner coma are crucial (Fulle et al. 1995). Therefore, we pay particular attention to the dust ejection velocity, which is assumed to have a wide distribution around the most probable values, and the dust ejection distribution, which is assumed to have a strong anisotropy peaked towards the sun. To compute the impact velocity in the probe reference frame, the rigorous keplerian orbit of each grain is considered taking into account aberrations due to the probe orbital velocity. We analyse the dependence of the results on the probe orbit parameters, such as true anomaly, probe–nucleus distance, orbit node and inclination. Computations are performed for the six main directions of the probe reference frame and for different values of the acceptance angle. The only way to collect direct grains is to point towards the nucleus; the mass collected in this direction is almost independent of the acceptance angle and of the time evolution of dust loss rate. A strong dependence of the collected dust mass on node and inclination is evidenced. By assuming an acceptance angle of $40^{∘}$, the flux of reflected grains received in the two directions perpendicular to the probe orbit is higher than that in the nucleus direction, for 42% of randomly oriented probe orbits. The value increases up to 56% when the acceptance angle in the directions perpendicular to the probe orbit is increased up to $80^{∘}$. The dust ejection anisotropy produces a strong dependence of the fluxes on the probe anomaly. For reflected grains, the fluences show relevant depletions at the largest masses, due to dust orbital effects, and the collected masses strongly depend on the acceptance angle and on the time evolution of the dust loss rate. The total dust fluxes are evaluated by assuming a half sphere field of view (corresponding to an acceptance angle of $180^{∘}$).