Understanding the growth mechanism in molecular organic thin films is fundamental to their applications in organic electronics. We present an extensive study of the growth mechanism of pentacene thin films on silicon dioxide (SiO₂) using atomic force microscopy. For a fixed substrate temperature T_s, the deposition rate κ is found to be a key parameter in controlling the nucleation density in the submonolayer regime and hence transport properties in the first layer of the organic field effect transistors. At a fixed T_s=338 K the maximum number of pentacene islands per unit area N follows the scaling law N∝κ^δ with δ=1.16±0.10. A mechanism of homogeneous nucleation followed by diffusive growth accounts for this behavior and allows us to estimate the critical nucleus size of the pentacene islands. The results obtained from a statistical analysis of the island size distribution are fully consistent with a phenomenological capture zone model. The validity of this model depends on the extent of reevaporation of pentacene admolecules during deposition, which is moderated by the deposition rate. We demonstrate that the rate dependence of island nucleation has important implications for the density of grain boundaries, which may play an important role in the transport mechanism