A theoretical and computational study of a tokamak boundary in contact with a limiter is given. Parallel field flows of plasma and heat induced by the sheath conditions at the limiter are treated with model sources and sinks in the cross-field transport equations. A charge-exchange neutral code is used for the re-cycled neutrals. It is found that the boundary conditions at the limiter radius have little effect on the energy flow to the boundary unless the ionization zone is well attached to the limiter. Exemplary heuristic boundary conditions useful for transport codes are given. The partitions of particle and energy flow to the limiter and wall are discussed.