Growth of metal nanowires from solution is a promising "bottom-up" method which can represent an efficient alternative to classical lithography. Here we present a dielectrophoretic growth of nanowires on an amorphous glass substrate in a solution containing Pt-complexes. Aiming at a controlled growth of straight and as thin as possible wires, the growth process is investigated both in theory and experiment. The metallic nanowire tip is modeled as a sphere electrode. The model includes the dielectrophoretic force on uncharged metal complexes as well as their diffusion in the solution. Experimental data suggest that the deposition process traverses from reaction-limited to diffusion-limited when going from low to high temperatures. Possible reasons for the rate limitation are discussed. Potassium ions in the solution are found to have a great influence on the deposition rate. Finally, we compare the experimentally measured growth velocities with those theoretically calculated.