In the current work, the Monte Carlo simulation method was applied to ethylene polymerization over Ziegler–Natta catalysts. As expected, polymerization over each center of a Ziegler–Natta catalyst leads to a polymer having a Schultz–Flory molecular weight distribution. Notwithstanding, the total molecular weight distribution obtained by all catalyst centers together is at least twice as broad as that of each center. As another interesting finding, the introduction of hydrogen to the reaction deactivates the catalyst active centers and thereby reduces the catalyst activity. Nevertheless, it does not mainly affect the polymerization kinetics. In addition, the polymer molecular weight falls as hydrogen is added to the reaction since it acts as a strong transfer agent. The same effect is seen when cocatalyst concentration increases. Hydrogen also widens the polymer molecular weight distribution. © 2008 Wiley Periodicals, Inc. Int J Chem Kinet 41: 45–56, 2009