Nanoparticle formation by laser ablation in liquids is studied numerically. We investigate such processes as cluster ejection, cluster nucleation, and aggregation. First, laser plume formation, its expansion, and confinement by the liquid are considered. These processes are connected with the formation of two shock waves: one moving inside the solid and the second one propagating in the liquid. If short and ultrashort laser pulses are used, the created plasma plume does not absorb laser radiation. In this case, a larger energy fraction is transferred into the solid during much shorter time, so that the ablation process is explosive. As a result, cluster precursors are ejected directly from the target, and the created plasma is confined to a smaller volume. Shorter laser pulses thus provide more favorable conditions for nanoparticle formation. In addition to the following short plasma expansion stage, a much longer aggregation process occurring in the liquid phase is found to affect the final size distribution.