We study the process of cluster formation at extreme supersaturations and identify the temperature-supersaturation domain where evaporation can be neglected resulting in a barrierless process with kinetics dominated by the dimer formation. The cluster size distribution obeys the coalescence equation with the pressure-temperature-dependent association rate coefficients ki, j. In view of the crucial role played by kinetics under these extreme conditions, the values of these coefficients calculated within the free molecular collision model are insufficient for the prediction of the nucleation rate and cluster distribution. An alternative is the use of ki, j obtained from the ab initio calculations. We apply these considerations to the analysis of recent water nucleation experiments in the postnozzle flow of a Laval nozzle. Theoretical predictions of nucleation rate are in an excellent agreement with experiment. At the same time, there is a discrepancy in the densities of small clusters. The latter can be attributed to the difference in ki, j extracted from the experimental data and those resulted from the ab initio calculations.