  We consider the Bak-Tang-Wiesenfeld sandpile model on square lattices in
different dimensions (D>=6). A finite size scaling analysis of the avalanche
probability distributions yields the values of the distribution exponents, the
dynamical exponent, and the dimension of the avalanches. Above the upper
critical dimension D_u=4 the exponents equal the known mean field values. An
analysis of the area probability distributions indicates that the avalanches
are fractal above the critical dimension.
