  This paper presents a comprehensive analysis of simple models useful to
analyze the growth of nanostructures obtained by cluster deposition. After
detailing the potential interest of nanostructures, I extensively study the
first stages of growth (the submonolayer regime) by kinetic Monte-Carlo
simulations. These simulations are performed in a wide variety of experimental
situations : complete condensation, growth with reevaporation, nucleation on
defects, total or null cluster-cluster coalescence... The main scope of the
paper is to help experimentalists analyzing their data to deduce which of those
processes are important and to quantify them. A software including all these
simulation programs is available at no cost on request to the author. I
carefully discuss experiments of growth from cluster beams and show how the
mobility of the clusters on the surface can be measured : surprisingly high
values are found. An important issue for future technological applications of
cluster deposition is the relation between the size of the incident clusters
and the size of the islands obtained on the substrate. An approximate formula
which gives the ratio of the two sizes as a function of the melting temperature
of the material deposited is given. Finally, I study the atomic mechanisms
which can explain the diffusion of the clusters on a substrate and the result
of their mutual interaction (simple juxtaposition, partial or total
coalescence...)
