  A simple model of epitaxial growth proposed by Wolf and Villain is
investigated using extensive computer simulations. We find an unexpectedly
complex crossover behavior of the original model in both 1+1 and 2+1
dimensions. A crossover from the effective growth exponent $\beta_{\rm
eff}\!\approx\!0.37$ to $\beta_{\rm eff}\!\approx\!0.33$ is observed in 1+1
dimensions, whereas additional crossovers, which we believe are to the scaling
behavior of an Edwards--Wilkinson type, are observed in both 1+1 and 2+1
dimensions. Anomalous scaling due to power--law growth of the average step
height is found in 1+1 D, and also at short time and length scales in 2+1~D.
The roughness exponents $\zeta_{\rm eff}^{\rm c}$ obtained from the
height--height correlation functions in 1+1~D ($\approx\!3/4$) and 2+1~D
($\approx\!2/3$) cannot be simultaneously explained by any of the continuum
equations proposed so far to describe epitaxial growth.
