Smoothed particle hydrodynamics (SPH) is used to estimate accretion rates of mass, linear and angular momentum in a binary system where one component undergoes mass loss through a wind. Physical parameters are chosen such as to model the alleged binary precursors of barium stars, whose chemical peculiarities are believed to result from the accretion of the wind from a companion formerly on the asymptotic giant branch (AGB). The binary system modelled consists of a 3 solar masses AGB star on the main sequence, in a 3AU circular orbit. Three-dimensional simulations are performed for gases with polytropic indices gamma=1, 1.1 and 1.5, to bracket more realistic situations that would include radiative cooling. Mass accretion rates are found to depend on resolution and we estimate typical values of 1-2% for the gamma=1.5 case and 8% for the other models. The highest resolution obtained (with 400k particles) corresponds to an accretor of linear size 16 solar radii. Despite being (in the gamma = 1.5 case) about ten times smaller than theoretical estimates based on the Bondi-Hoyle prescription, the SPH accretion rates remain large enough to explain the pollution of barium stars. Uncertainties in the current SPH rates remain however, due to the simplified treatment of the wind acceleration mechanism, as well as to the absence of any cooling prescription and to the limited numerical resolution. Angular momentum transfer leads to significant spin up of the accretor and can account for the rapid rotation of HD165141, a barium star with a young white dwarf companion and a rotation rate unusually large among K giants.

13 pages, mn style, 5 figures, to be published by MNRAS