The molecular-level processes responsible for fractal-dendritic growth of second-layer C60 islands on large and compact first-layer C60 islands deposited on graphite substrate are investigated by a combination of scanning tunneling microscopy (STM) and kinetic Monte Carlo (kMC) simulations. Molecular dynamics (MD) simulations are performed to determine the activation barriers and jump rates for diffusion of C60 molecules on a C60 layer. The rates of the thermally activated processes, determined in MD simulations, are used in kMC simulations performed to explore the connections between the elementary growth mechanisms and the shapes of the growing islands. The geometry of the underlying substrate is found to result in the formation of two characteristic molecular arrangements along the edges of the growing islands (A-step and B-step on a close-packed surface). The difference in the molecular mobility along the A-step and B-step configurations, along with the difference in the probability of a C60 molecule ...