A companion article by Tandon and Rosner (1999) showed that Monte-Carlo (MC) simulation methods can generate joint pdfs of particle volume, v, and surface area a, for coagulating populations of suspended nonspherical particles simultaneously sintering at finite rates. For continuum-regime Brownian coagulation at times longer than the characteristic coagulation time, a "self-preserving" asymptotic pdf shape was shown to extend to these bivariate populations, using the rescaled volume v/(v) over bar (t) and rescaled area a/(a) over bar (t) as "similarity" variables. This article considers the corresponding problem of coagulation in the "free-molecule" limit, relevant to the atmospheric pressure flame experiments of Xing et al. This combination of coagulation- and sintering-rate laws again leads to "self-preserving" rescaled jpdfs, explicitly time-independent for an isothermal environment again dependent on a Damkohler-like number, Dam(f) (ratio of coagulation time to fusion time). While flames are more complex than our idealized simulations, our present pdfs and associated "mixed moments, "capture important features of experimental results as one approaches the flame, especially evolution of a mean particle "shape factor," mean number of spherules per aggregate, and narrowness of the spread of spherule sizes. This agreement, coupled with the versatility of MC-methods for multistate variable particle population balances, encourages extensions leading to a versatile tractable, formalism for the developing field of sol reaction engineering.