The stochastic simulations of the polymer growth under different reaction conditions (temperature and pressure) have been performed for the ethylene polymerization processes catalyzed by late transition metal complexes. The processes catalyzed by the real Pd-based diimine catalyst have been studied on the basis of the energetics of elementary reactions (DFT-calculated and experimental). The simulations with systematically changed insertion barriers have also been performed to model the influence of different catalysts, going beyond diimine systems. In the case of diimine catalysts, the simulations reproduce the experimentally observed average number of branches as well as the temperature and pressure dependencies of the branching numbers. The results explain the microscopic origin of an opposite temperature effect observed for ethylene and propylene polymerization. Further, the simulations allow one to understand the different pressure effect observed for Pd- and Ni-based diimine catalysts. The model simulations give insight into the role of particular factors controlling the polyethylene branching. It has been found that an energy difference between the activation barriers for the primary and secondary insertions strongly influences the polymer microstructure. The results demonstrate that a wide range of polymer topologies can be potentially obtained from ethylene polymerizations with various single-site catalyst characterized by different energetics of the catalytic cycle. Thus, it seems to be possible to rationally design a catalyst producing a desired polyethylene microstructure.