The geometry of a total-internal-reflection (TIR) phase-conjugate mirror is investigated in the framework of a two-dimensional model, based on the solution of nonlinear material equations and the parabolic equations for electromagnetic radiation. The model self-consistently describes the evolution of incoherent scattering into the spatial structure of light corresponding to the operation of the TIR mirror. We analyze the dynamics of nonlinear reflectivity and conjugation fidelity and their dependence on parameters of the problem, the spatial structure of fields and the nonlinear refractive index, and the typical distortions in the phase-conjugate output of the TIR mirror. Theoretical predictions are confirmed experimentally.