A three-dimensional, quasiclassical analysis of the K+CHSI reaction and related reactions is performed. Hamilton's equations of motion are solved to obtain collision trajectories from which the reaction attributes are determined by Monte Carlo averaging over appropriately selected sets of initial conditions. Four different functional forms for the potential energy of interaction of the reacting species are examined. Comparisons are made of the total reaction cross section, the rotational and vibrational state distribution of the product molecule, the reaction energy distribution, the differential reaction cross section in both center-of-mass and laboratory coordinates, lie distribution of the final angular momentum between the molecule and the relative orbital motion, the degree of polarization of the final rotational angular momentum of the molecule, the behavior in the transition region, and the effect of mass changes on the reaction. Although most of the calculated results are not subject to direct experimental verification at present, the theoretical laboratory cross section can be compared with measured values. It is found that three of the surfaces studied yield a laboratory differential cross section for K+CHal in reasonable correspondence with the available experimental measurements, which are insufficient as yet to permit any distinction between these surfaces. Analysis of the behavior in the transition region shows that the reaction on these surfaces proceeds through a simple collision mechanism in which the three particles interact for only a very short time. The very different results obtained from a special surface in which a collision complex is formed are given for comparison.