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Surface growth in random media is usually governed by both the surfacetension and the random local forces. Simulations on lattices mimic the formerby imposing a maximum gradient $m$ on the surface heights, and the latter bysite-dependent random growth probabilities. Here we consider the limit $m \to\infty$, where the surface grows at the site with minimal random number, {\itindependent} of its neighbors. The resulting height distribution obeys a simplescaling law, which is destroyed when local surface tension is included. Ourmodel is equivalent to Yee's simplification of the Bak-Sneppen model for theextinction of biological species, where the height represents the number oftimes a biological species is exchanged.Comment: 11 pages including numerous figures; for Int. J. Mod. Phys.

SCALING IN A SIMPLE MODEL FOR SURFACE GROWTH IN A RANDOM MEDIUM