Controlling the evolution of morphology and properties during the precipitation of mesoporous materials is a key technological challenge. This entails the scientific challenge of modelling and simulating a complex mesoscale kinetics. We present an original off-lattice Kinetic Monte Carlo approach to simulate various precipitation mechanisms at the mesoscale of nanoparticle aggregates. The simulations are based on novel coarse-grained rate expressions of nanopartice precipitation/dissolution, accounting for both solution chemistry and mechanical interactions. The precipitation of ordered and amorphous domains is simulated, showing how particle-particle and particle-substrate interactions determine various mechanisms: layer-by-layer precipitation, islands formation, Cahn and Avrami nucleation and growth, and gel-like precipitation. The simulations clarify how the total precipitation rate depends on the triggered mechanism, and therefore on solution chemistry and on mechanical interactions. This brings together chemical kinetics and nanoparticle simulations for a more fundamental understanding of mesostructure development, towards a computer-aided design of mesoporous materials.