  The absorbing "ricepile" model with stochastic toppling rules has been
numerically studied. Local limited, local unlimited, nonlocal limited and
nonlocal unlimited versions of the absorbing model have been investigated.
Transport properties and different dynamical regimes of all of the models have
been analysed, from the point of view of self organized criticality (SOC).
Phase transitions between different dynamical regimes were studied in detail.
It was shown, that the absorbing models belong to two different universality
classes.
