Hetrochain branching theory is applied to develop a matrix formula describing the weight-average molecular weights for the free-radical polymerization that involves simultaneous long-chain branching and random scission. The gel point is simply described as a point at which the largest eigenvalue of the matrix, M, which defines the chain connection statistics, reaches unity. The illustrative calculations show that the calculated results agree satisfactorily with those obtained from the Monte Carlo simulation method developed in the first part of this series. The present matrix formula is superior in the precision of the weight-average molecular weights and the gel point, while the Monte Carlo simulation technique can provide much more detailed information, and therefore, these two methods are nicely complementary. (C) 2001 John Wiley & Sons, Inc.