The degree of short chain branch (SCB) formation during ethylene polymerization catalyzed with nickel-diimine/trimethylaluminum. systems is a function of the relative rates of polymerization and catalyst chain walking. The proper choice of polymerization temperature (30-50 degreesC) and ethylene pressure (1.0-18.4 kgf cm(-2)) allows one to tailor make the SCB content of the polyethylene produced with these catalysts. Within such range, polyethylene can be prepared with 10-100 branches per 1000 carbon atoms in the backbone. The unique branch distribution, which mimics the one obtained in the copolymerization of ethylene and alpha -olefins, is described in detail using Monte-Carlo simulation of polymerization and chain walking. The four probability parameters used in the model were correlated to polymerization temperature, T, and ethylene concentration, [E]. With this model, it is possible to predict polyethylene microstructure as a function of T and [E]. The dependence of each parameter on these two polymerization conditions is helpful to clarify the mechanism of branch formation with these intriguing catalyst systems.