Polymer pyrolysis has emerged as a simple and versatile method to synthesize graphenoid (graphene like) materials with varying thickness and properties. The morphology of the thin film, especially the thickness, greatly affects the graphitizability (ability to from ordered graphene/ graphite) and thus the properties of the resulting graphenoid material. Using in situ current annealing inside a transmission electron microscope (TEM), we followed the thickness-dependent structural evolution of the polymer film with a special focus on thickness effects. Up to intermediate temperatures, the structural evolution during current annealing is similar to the evolution during thermal annealing of the thin films. At higher temperatures, thin samples form large graphene layers oriented parallel to the substrate, whereas in thick samples multi-walled cage-like structures are formed. MD simulations reveal a critical film thickness of 40 Å below which, the carbonized layers align parallel to the surface. For thicker samples, the orientation of the layers becomes increasingly misoriented starting from the surface to the center. This structural change can be attributed to the formation of bonded multi-layers from the initially unsaturated activated edges. The resulting cage-like structures are stable even during simulated annealing at temperatures as high as 3500 K. An atomistic understanding of the formation of these structures is presented. The results clearly indicate the critical effect of thickness on graphitizability of polymers and provide a new understanding of the structural evolution during pyrolysis.