Using the density-functional method and clusters modelling steps of (B)P(001) surfaces, chemisorption and desorption energies as well as related barriers are calculated for probable chemisorption structures formed by precursor molecules XZ(3) (X: B, Ga, In, P; Z: H, Me=CH3) during the metal-organic chemical vapour deposition (MOCVD). Reaction mechanisms, especially the stability of surface structures, the efficiency of the precursor molecules, and the rate-limiting steps, are obtained. In most cases, the final removal of hydrogen or methyl groups is the rate-limiting step. The deposition with hydrogen precursors (XH3) is faster than the analogous deposition with methyl precursors (XMe3) The deposition rate decreases from indium over gallium to boron. The rate of phosphorus deposition in surface dimers decreases from indium over gallium to boron dimers. Trimethylphosphine (TMP) is a less suitable precursor. Boron antisite deposition and formation of BGa and Bin alloys is less probable. The formation of an elementary boron phase by BH3 is less probable and can be fully prevented by using trimethylboron (TMB) precursors. The differences in the reaction behaviour in comparison with (BInGa)As, investigated previously, are discussed. (C) 2009 Elsevier B.V. All rights reserved.