Turbostratic carbon nanotubes (CNTs) and nanofibers (CNFs) are synthesized by chemical vapor deposition using titania nanoparticle catalysts, and a quantitative lift-off model is developed to explain CNT and CNF growth. Micron-scale long turbostratic CNTs and CNFs were observed when acetylene is utilized as a carbon feedstock, and an alumina substrate was incorporated to improve the homogeneity of catalyst distribution. Turbostratic CNTs/CNFs are always found attached to nanoparticle corners, in the absence of the graphitic cage that is typically observed with metal nanoparticle-mediated growth. The observed morphology in turbostratic CNTs/CNFs supports a model in which several layers of graphene lift off from high-curvature corners of the titania nanoparticle catalysts. This model explains a key feature, which differentiates the growth of turbostratic CNTs/CNFs via non-metallic nanoparticles from growth using standard metal nanoparticle catalysts. The observed CNT/CNF growth and the accompanying model can impact the assessment of other metal-oxide nanoparticle catalysts, with the findings here contributing to a metal-free synthesis of turbostratic CNTs/CNFs.