  We introduce spatial inhomogeneities (boundaries) in a random neighbor
version of the Olami, Feder and Christensen model [Phys. Rev. Lett. 68, 1244
(1992)] and study the distributions of avalanches starting both from the bulk
and from the boundaries of the system. Because of their clear geophysical
interpretation, two different boundary conditions have been considered (named
free and open, respectively). In both cases the bulk distribution is described
by the exponent $\tau \simeq {3/2}$. Boundary distributions are instead
characterized by two different exponents $\tau ' \simeq {3/2}$ and $\tau '
\simeq {7/4}$, for free and open boundary conditions, respectively. These
exponents indicate that the mean-field behavior of this model is correctly
described by a recently proposed inhomogeneous form of critical branching
process.
