Semiconductor nanowires (NWs) are promising building blocks for nano-electronic and nano-optoelectronic devices, such as field effect transistors, photodetectors and LEDs. However, it is still challenging to integrate NWs into practical devices that require planar arrays. During the past few years, our group has significantly advanced the guided growth approach to produce horizontal NWs with controlled directions and crystallographic orientations. In order to predict and fully control these growth directions and crystallographic orientation, an understanding of the mechanism of the guided NWs growth is needed. Herein, we consider theoretically the growth kinetics of planar ZnSe nanowires grown on c- plane sapphire. Non-monotonic dependence of the NW growth rate versus radius showing increasing radius dependence for thin NWs and decreasing dependence for wider NWs is similar to that typically observed for vertical NWs. In the latter case, such dependence has previously been explained by a competition of the Gibbs-Thomson effect suppressing the vapor-liquid-solid (VLS) growth of NWs and the diffusion-induced growth effects that lead to inverse length-radius correlation. We show some important differences in kinetics processes driving the VLS growth of planar versus vertical NWs and derive analytical equation for the growth rate of planar NWs that combines contributions from all possible kinetic pathways of such growth.