  The recently introduced self-organizing height-arrow (HA) model is
numerically investigated on the square lattice and analytically on the Bethe
lattice. The concentration of occupied sites and critical exponents of
distributions of avalanches are evaluated for two slightly different versions
of the model. The obtained exponents for distributions of avalanches by mass,
area, duration and appropriate fractal dimensions are close to those for the
BTW model, which suggests that the HA model belongs to the same universality
class. For comparison, the concentration of occupied sites in the HA model is
calculated exactly on the Bethe lattice of coordination number $q=4$ as well.
