The growth of polycyclic aromatic hydrocarbons (PAHs) is in many areas of combustion and pyrolysis of hydrocarbons an inconvenient side effect that warrants an extensive investigation of the underlying reaction mechanism, which is known to be a cascade of radical reactions. Herein, the focus lies on one of the key reaction classes within the coke formation process: hydrogen abstraction reactions induced by a methyl radical from methylated benzenoid species. It has been shown previously that hydrogen abstractions determine the global PAH formation rate. In particular, the influence of the polyaromatic environment on the thermodynamic and kinetic properties is the subject of a thorough exploration. Reaction enthalpies at 298 K, reaction barriers at 0 K, rate constants, and kinetic parameters (within the temperature interval 700-1100 K) are calculated by using B3LYP/6-31+G(d,p) geometries and BMK/6-311+G(3df,2p) single-point energies. This level of theory has been validated with available experimental data for the abstraction at toluene. The enhanced stability of the product benzylic radicals and its influence on the reaction enthalpies is highlighted. Corrections for tunneling effects and hindered (or free) rotations of the methyl group are taken into account. The largest spreading in thermochemical and kinetic data is observed in the series of linear acenes, and a normal reactivity-enthalpy relationship is obtained. The abstraction of a methyl hydrogen atom at one of the center rings of large methylated acenes is largely preferred. Geometrical and electronic aspects lie at the basis of this striking feature. Comparison with hydrogen abstractions leading to arylic radicals is also made.