It is shown that limited surface diffusion may strongly modify propert
ies of the film surface. For linear samples, when some analytical resu
lts are known for random deposition, the fractal dimension D of the su
rface is discussed. Model predictions and computer simulation shows th
at D < 1 for the static case, when assembly of clusters is scanned. Th
e surface is smoother for positive binding energy between atoms, and m
ore rough otherwise. With zero binding energy, analytical results of r
andom growth is recovered.