  Kardar-Parisi-Zhang interface depinning with quenched noise is studied in an
ensemble that leads to self-organized criticality in the quenched
Edwards-Wilkinson (QEW) universality class and related sandpile models. An
interface is pinned at the boundaries, and a slowly increasing external drive
is added to compensate for the pinning. The ensuing interface behavior
describes the integrated toppling activity history of a QKPZ cellular
automaton. The avalanche picture consists of several phases depending on the
relative importance of the terms in the interface equation. The SOC state is
more complicated than in the QEW case and it is not related to the properties
of the bulk depinning transition.
