Numerical simulations of the hydrodynamics and mass transfer involved in the rapid growth of very large potassium di-hydrogen phosphate (KDP) crystals with linear dimensions up to 60 cm and masses greater than 270 kg have been performed. The computational geometry corresponds very closely to the 1000-1 crystallizers currently in use at Lawrence Livermore National Laboratory (LLNL) for the growth of KDP crystals for the National Ignition Facility (NIF). In a related paper (J. Crystal Growth 222 (2000) 263), the temporal and spatial character of the three-dimensional, time-dependent, turbulent flow field was discussed. This paper presents the corresponding results concerning the mass transfer occurring at the crystal surface during the rapid growth process. Emphasis is placed on studying the surface concentration or supersaturation distribution, since it is critically involved in the processes of morphological instability and inclusion formation. The temporal and spatial evolution of the surface supersaturation is studied as a function of crystal size, growth rate, and rotation conditions. (C) 2003 Elsevier B.V. All rights reserved.