The natural tendency of carbon nanotubes (CNTs) to agglomerate is an underlying reason that prevents the realization of their full potential. On the other hand, covalent functionalization of CNTs to control dispersion leads to disruption of π-conjugation in CNTs and the non-covalent functionalization leads to a weak CNT-polymer interface. To overcome these challenges, we describe the characteristics of fostering of direct nucleation of polymers on nanostructured carbon (CNTs of diameters (~2-200 nm), carbon nanofibers (~200-300 nm), and graphene), which culminates in interfacial adhesion, resulting from electrostatic and van der Waals interaction in the hybrid nanostructured carbon-polymer architecture. Furthermore, the structure is tunable through a change in undercooling. High density polyethylene and polypropylene were selected as two model polymers and two sets of experiments were carried out. The first set of experiments was carried out using CNTs of diameter ~2-5 nm to explore the effect of undercooling and polymer concentration. The second set of experiments was focused on studying the effect of dimensionality on geometrical confinements. The periodic crystallization of polyethylene on small diameter CNTs is demonstrated to be a consequence of the geometrical confinement effect, rather than epitaxy, such that petal-like disks nucleate on large diameter CNTs, carbon nanofibers, and graphene. The application of the process is illustrated in terms of fabricating a system for cellular uptake and bioimaging.