  The effect of bulk dissipation on non critical sandpile models is studied
using both multifractal and finite size scaling analyses. We show numerically
that the local limited (LL) model exhibits a crossover from multifractal to
self-similar behavior as the control parameters $h_{ext}$ and $\epsilon$ turn
towards their critical values, i.e. $h_{ext} \to 0^+ $ and $\epsilon \to
\epsilon_c$. The critical exponents are not universal and exhibit a continuous
variation with $\epsilon$. On the other hand, the finite size effects for the
local unlimited (LU), non local limited (NLL), and non local unlimited (NLU)
models are well described by the multifractal analysis for all values of
dissipation rate $\epsilon$. The space-time avalanche structure is studied in
order to give a deeper understanding of the finite size effects and the origin
of the crossover behavior. This result is confirmed by the calculation of the
susceptibility.
