Laser-produced nanoparticles have found many applications in bio-photonics, medicine and in the development of photovolvatic cells. Many experiments have been performed demonstrating the formation of these particles from solid targets in vacuum, in the presence of a gas or a liquid. However, it is still difficult to predict the size distribution of these particles. Therefore, we have performed an extensive numerical modeling of the involved physical processes. The developed models allow us to compare the relative contribution of several processes involved in the cluster production by laser ablation: (i) direct cluster ejection from a target under rapid laser interaction, (ii) condensation/evaporation; (iii) fragmentation/aggregation processes during cluster diffusion; and (iv) diffusion and coalescence if nanoparticles are deposited on a substrate. The calculation results of both hydrodynamic and molecular dynamics simulations demonstrate that an exposure of a target to a short or ultra-short laser pulse leads to an explosive target decomposition and to the ejection of nanoparticles. These cluster precursors are formed during rapid target expansion through both thermal and mechanical processes. Collisions with background species affect the cluster size distribution. The influences of the parameters, such as initial cluster temperature and size, background temperature and density, on the cluster evolution are analyzed. Laser-induced phase explosion process affects the formation of small surface structures, obtained with small number of shots. However, the non-resonant “conical” surface structures with the mean size as large as several micrometers are formed due to the presence of harder less absorbing centers. These obtained results can be used to explain many recent experimental observations.