The random sampling technique discussed in part 1 of this series’ is used to investigate the molecular weight distribution (MWD) change during random scission reactions of the polymers with multiple branches. By application of the concept of the random sampling technique to the Monte Carlo method, one obtains a very powerful simulation method that can be applied to the random degradation of virtually any type of branched polymer. Suppose branched polymers are formed first by randomly combining linear polymer molecules, and then these branched polymer molecules are used for the random degradation reactions (branching --> degradation). If the processes of branching and degradation are interchangeable, then the same MWD can be obtained from the sequence of processes, degradation --> branching. In contrast with random cross-linking and degradation, the processes are not interchangeable except when all of the primary chains possess the most probable distribution with randomly distributed branch points. The MWDs given by the random branching of primary chains with the most probable distribution provide the limiting distributions to which polymers with multiple branches approach as the extent of the scission reaction increases, irrespective of the initial MWD including nonrandomly branched polymers. An analytical expression for such a limiting MWD is derived by the application of the random sampling technique.