The results of combined DFT/stochastic studies on the mechanism of ethylene polymerization catalyzed by a neutral Ni-anilinotropone complex are presented. The generation of active species by phosphine dissociation and chain propagation and chain isomerization reactions have been investigated. The alternative methyl acrylate binding modes have also been studied. Further, the DFT-calculated energetics of the elementary reactions have been used to model the influence of the reaction conditions (T, P) on the branching/microstructure of polyethylenes produced in this process. The model and real catalysts (N<^>O-Ni; N<^>O = -N(Ar)-(C7H5)-O-,with Ar = H and Ar =C6H3(i-Pr)(2), respectively) have been considered to account for the electronic and steric effects. The presence of two cis/trans isomers for all the reactions has been considered. The results indicate that for the real anilinotropone catalyst the phosphine dissocciation is less endothermic (22 kcal/mol) than for the corresponding salicylaldiminato system (29 kcal/mol). The more branched alkyl agostic complexes are found to be more stable than the less branched and the linear isomers, while the stability order for the olefin-alkyl complexes is opposite. Thus, the stability of the alkyl complexes shifts the equilibrium toward formation of the branched species, while the stability of ethylene complexes favors formation of linear structures. The DFT results show that the energetically preferred pathways for the chain propagation and isomerization reactions start from the higher energy cis/trans isomers (with the alkyl positioned trans to the N atom on the catalyst). The preferred isomerization reactions have very low barriers (2.4-4.5 kcal/mol for different alkyl species). Along these pathways the unusually stable olefin-hydride complexes are formed, some of them being more stable (by 1.5-3 kcal/mol) than the alkyl agostic complexes. The results of the calculations for the methyl acrylate complexes confirm the high tolerance of the anilinotropone catalyst toward polar groups: the pi-complexes are more stable by 8-13 kcal/mol than the systems with the acrylate molecule bound by its carbonyl oxygen. This functional group tolerance is larger than for the Grubbs catalyst. Also, the acrylate pi-complexation energies are less affected by the steric bulk than in the case of salicylamidato catalysts and the diimine catalysts. Finally, the results of the stochastic simulations quantitatively reproduce the experimental trends in the temperature and pressure dependence of the average number of branches. In addition, the stochastic simulations provide detailed information about the variations in the topology of polyethylenes produced under different conditions.