Carbon nanostructures formed through physical synthesis come in a variety of sizes and shapes. With the end goal of rationalizing synthetic pathways of carbon nanostructures as a function of tunable parameters in the synthesis, we investigate how the initial density and quench rate influence the morphology of carbon nanostructures obtained from the cooling of a gas of atomic carbon by molecular dynamics simulations. For the structural analysis, we combine classical order parameters with a data-driven approach based on local density descriptors and kernel similarity measurements. Aided by this complementary set of tools, we describe in detail the formation of carbon nanostructures from the gas phase. Their formation proceeds through the nucleation of small liquid carbon nanoclusters followed by growth into unique objects. We find that ordered structures can only be obtained at certain quenching rates and that among those, fullerene-like particles are favored at intermediate densities while nanotubes-like structures require higher initial densities. & COPY; XXXX CEA. Elsevier