Graphene and carbon nanotubes (CNTs), allotropes of hexagonal sp2-hybridized carbon, were some of the first nanomaterials discovered and had attracted attention since. Current theoretical understanding of the formation processes for those materials mainly relies on thermodynamic principles while kinetics is mostly overlooked. This work proposes a hybrid Kinetic Monte Carlo (KMC) method to represent the kinetic growth of atomically resolved systems of sp2-hybridized carbon at reasonable computational costs. This novel and comprehensive model is used to investigate the growth of grain boundaries (GB) - disordered regions between misoriented grains in polycrystalline graphene. Unlike all previous studies, this work is focused on the dynamic formation of GBs. This model demonstrates a characteristic of the initial configuration that determines the final structure of the GB, resolving a long outstanding discrepancy between theoretical predictions and experimental observations. Additionally, the possibility of asymmetry of graphene GBs is considered. The maximum deviation from symmetry is found not to exceed 12°. More importantly, due to probabilistic nature of GB directions, experimental differentiation between global and local asymmetry was found to be impossible. Extended to three-dimensions and combined with the representation of catalyst particle through Lennard-Jones sphere, the hybrid KMC model presents a computationally efficient simulation method for CNT nucleation. Analysis of collected statistically relevant data (6x104 tubes per parameter set) demonstrated a correlation between catalyst-tube interaction and chiral preference of nucleated CNTs, suggesting possible future routes towards chiral selectivity. Investigating the recent experimental success in chirally selective growth of CNT on the solid Co7W6 catalyst, we discovered energetical preference towards CNT edge with segregated zigzag and armchair facets. This new edge structure mandates growth patterns that lead to defect-induced pooling at observed (12,6) chirality. The KMC simulations predict the (12,6) abundance to be around 90% that closely matches experimental results. Finally, the radial stability of the large diameter single- and double-walled CNT is considered. Using experimental data collected by our collaborators, the critical size of the CNT, beyond which nanotube collapses forming closed-edge graphene nanoribbons, was determined to be 2.8 nm for a single-walled CNT and 4.0 nm for a double-walled CNT.