Aims: We investigate Bondi-Hoyle-Lyttleton accretion onto a black hole for ultra-relativistic flows, and how flow features are affected by density perturbations, upstream fluid velocity, and black hole spin.

Methods: We use high-resolution shock-capturing (HRSC) schemes solved on curvilinear overlapping grids as demonstrated in a previous publication.

Results: We demonstrate the quantitative dependence of the shock-angle and mass accretion rate on black hole spin, upstream fluid velocity, and density perturbations. We also demonstrate the qualitative dependence of the accretion region and flow features on the same parameters.

Conclusions: We find that the mass accretion rate does not depend strongly on these parameters, and most of the difference in flow is seen in the shock angle and general flow patterns close to the black-hole, as previously predicted by lower-dimensional simulations. Moreover, we demonstrate independence of initial conditions in that a steady flow around a non-spinning black-hole which suddenly starts to spin will converge to the same flow pattern as if the black-hole had been spinning initially.