The theory of carbon transport in a plasma boundary layer is important for understanding the impurity penetration, and carbon and hydrogen recycling, in tokamaks using carbon compounds as limiters and as wall coatings. Neutral carbon kinetics and transport at the edge of plasma devices where chemical release is a source of carbon are modeled. Plasma reactions with carbon and hydrocarbons are important for such modeling, and these collisional processes are summarized. Combining the reaction schemes and kinetics in the DEGAS code makes it possible to treat the neutral transport at the plasma boundary layer. Results of such modeling of the atomic carbon and methane distribution at the edge are presented for comparison with recent carbon probe experiments performed on the Divertor and Injection Tokamak Experiment (DITE). The density distribution of carbon impurities at the edge is found to vary with edge conditions, with that of each daughter product in the breakdown being much broader and deeper than the parent molecule. Furthermore, the energy of the carbon atoms released from methane is considerably higher, on average, than the energy at which the methane is released from the wall or limiter. At high densities recycling can play an important role in the transport, and as much as 30% of the carbon flux might be due to recycling in the DITE configuration. Recycling can also be important for understanding the erosion and redeposition of carbon on limiters, which, while apparently insignificant in the DITE carbon probe experiments, might be important for limiters on the Tokamak Fusion Test Reactor.