  Surface growth in random media is usually governed by both the surface
tension and the random local forces. Simulations on lattices mimic the former
by imposing a maximum gradient $m$ on the surface heights, and the latter by
site-dependent random growth probabilities. Here we consider the limit $m \to
\infty$, where the surface grows at the site with minimal random number, {\it
independent} of its neighbors. The resulting height distribution obeys a simple
scaling law, which is destroyed when local surface tension is included. Our
model is equivalent to Yee's simplification of the Bak-Sneppen model for the
extinction of biological species, where the height represents the number of
times a biological species is exchanged.
