A detailed study of the reaction kinetics of the plasma-assisted molecular beam epitaxy(MBE)growth of the n-type semiconducting oxide Ga2O3 is presented. The growth rate as a function of gallium flux is measured in situ by laser reflectometry at different growth temperatures (TG) and gallium-to-oxygen ratios (rGa). The flux of the suboxide Ga2O desorbed off the growth surface is identified in situ by line-of-sight quadrupole mass spectroscopy. The measurements reveal the influence of TG and rGa on the competing formation of Ga2O3 and desorption of Ga2O resulting in three different growth regimes: (i) Ga transport limited, (ii) Ga2O desorption limited, and (iii) O transport limited. As a result, we present a growth diagram of gallium oxide. This diagram illustrates the regimes of complete, partial, and no Ga incorporation as a function of TG and rGa, and thus provides guidance for the MBEgrowth of Ga2O3.