The cellular automaton model is used to simulate diffusion (with activation migration energy Era) and aggregation (with full capture and binding energy Eo) of point particles in 2D. A sharp dynamical phase transition is found that separates a dynamical phase (with many small aggregates and mobile particles, which are homogeneously distributed) and a static phase (with few big pileups of aggregates and many immobile particles, which are inhomogeneously distributed). It is similar to the Biham-Levine-Middleton jamming transition (O. Biham, A.A. Middleton and D. Levine, Phys. Rev. A 46 (1992) R6124), which is a function of the particle concentration. In addition to this, we found that the transition is a function of balance between energies E,,, and Eb. The main parameters, namely, concentration of free movable particles, the number of aggregates, the number of pile-ups of aggregates, undergo sharp changes in the narrow range of K = exp( ( Eh--Em)/kBT). Self-organization effects and mechanisms of selection between inhomogeneities are studied and discussed. Manifestations of the transition in real physical systems (two-dimensional surface nanostructures, non-crystallographic defect structures, stone ripples, etc.) are discussed.