A classical phase space theory procedure for estimating product state distributions for "barrierless" dissociations is described. The distributions are determined in terms of an average over the available phase-space on a fixed dividing surface of the function describing the distribution of interest. The use of a weighting function corresponding to the contribution of each randomly sampled phase space point to the number of available states, as in related state counting algorithms, provides an efficient route to the determination of any particular product state distribution of correlation. The coordinates employed in this sampling are the Euler angles, describing the orientation in space of each of the fragments and of the line of centers connecting the two fragments, and their conjugate momenta. Sample applications focus on the determination of the vector correlation between the angular momentum of one fragment and the relative velocity of the fragments for the dissociations of 2-chloro-2-nitrosopropane (CNP), NCCN, and CF3NO. Comparisons with the corresponding experimental measurements for the CNP and NCCN dissociations provide further evidence for the presence of important dynamical effects in these dissociations. The calculations for CF3NO are presented with the hope of motivating an experimental verification of the predicted strong v-j correlation for the CF3 fragment in combination with the weak correlation for the NO fragment. Overall, these phase space theory results are found to provide a useful reference for the interpretation of experimental results.