Results of time dependent simulations of growth of bulk binary III-V crystals by current controlled liquid phase electroepitaxy (LPEE) are reported using GaAs as an example. Without any electrical current the LPEE system is isothermal, kept at 1073 K, thus no growth occurs. The electric current density of 10 A/cm(2) leads to ohmic heating of the entire system, Peltier cooling of the Ga-GaAs(seed) interface and electromigration of As species in liquid Ga. Neither Peltier nor Joule effects are considered at the source/solution interface since in the configuration chosen the electric current bypasses the source crystal. The Peltier induced cooling and electromigration of As induce growth of GaAs, originally at the rate of 0.5 mu m/min. As the growth proceeds the Peltier cooling starts to be compensated by Joule heating inside the crystal grown. Thus, the growth slows down and finally the average growth rate decreases to zero. It is shown that the LPEE growth is strongly time dependent, leading to the change in crystallization front, reflecting the slowest growth rate at the center of the crucible and the fastest close to the crucible wall. The temperature, As concentration convection and electric current distribution are presented showing their influence on the surface morphology of growing GaAs crystal. (C) 2010 Elsevier B.V. All rights reserved.