We stuy the process of cluster formation at extreme supersaturations an ientify the temperature-supersaturation omain where evaporation can be neglecte resulting in a barrierless process with kinetics ominate by the imer formation. The cluster size istribution obeys the coalescence equation with the pressure-temperature-epenent association rate coefficients ki, j. In view of the crucial role playe by kinetics uner these extreme conitions, the values of these coefficients calculate within the free molecular collision moel are insufficient for the preiction of the nucleation rate an cluster istribution. An alternative is the use of ki, j obtaine from the ab initio calculations. We apply these consierations to the analysis of recent water nucleation experiments in the postnozzle flow of a Laval nozzle. Theoretical preictions of nucleation rate are in an excellent agreement with experiment. At the same time, there is a iscrepancy in the ensities of small clusters. The latter can be attribute to the ifference in ki, j extracte from the experimental ata an those resulte from the ab initio calculations.