A directed dissipative sandpile model is studied in two dimensions. Numeric
al results indicate that the long time steady states of this model are crit
ical when grains are dropped only at the top, or everywhere. The critical b
ehavior is mean-field-like. We discuss the role of infinite avalanches of d
issipative models in periodic systems in determining the critical behavior
of same models in open systems. [S1063-651X(99)50811-8].