We study both submonolayer and multilayer growth in a model of thin-fi
lm growth appropriate for the case in which the deposited material is
''incompatible'' with the substrate in the sense that the deposited at
oms do not wet the substrate. We find that the scaling behavior of the
monomer and island densities, when considered as functions of the fir
st layer coverage theta(1) and the ratio D/F of monomer diffusion rate
D to the deposition flux F is similar to that for ordinary submonolay
er growth. However, the surface morphology is very different. In parti
cular, the substrate remains incompletely covered, with large grooves
between the three-dimensional islands up to fairly large coverage. On
the other hand, the nonwetting (hopping-up) process and the step barri
er yield dimer and trimer mobilities which lead to a three-dimensional
island-size-distribution scaling function which is dependent on the v
alues of D/F. For D/F = 10(7) and low coverage, the scaling function w
as found to be similar to that for submonolayer growth with critical i
sland size i=2, while for D/F = 10(8), it appears to be similar to tha
t for i=3.