InGaAs is a potential candidate for Si replacement in upcoming advanced technological nodes because of its excellent electron transport properties and relatively low interface defect density in dielectric gate stacks. Therefore, integrating InGaAs devices with the established Si platforms is highly important. Using template-assisted selective epitaxy (TASE), InGaAs nanowires can be monolithically integrated with high crystal quality, although the mechanisms of group III incorporation in this ternary material have not been thoroughly investigated. Here we present a detailed study of the compositional variations of InGaAs nanostructures epitaxially grown on Si(111) and Silicon-on-insulator substrates by TASE. We present a combination of XRD data and detailed EELS maps and find that the final Ga/In chemical composition depends strongly on both growth parameters and the growth facet type, leading to complex compositional sub-structures throughout the crystals. We can further conclude that the composition is governed by the facet-dependent chemical reaction rates at low temperature and low V/III ratio, while at higher temperature and V/III ratio, the incorporation is transport limited. In this case we see indications that the transport is a competition between Knudsen flow and surface diffusion.