The formation of H-2 in the interstellar medium proceeds on the surfaces of silicate or carbonaceous particles. To get a deeper insight of its formation on the latter substrate, this Letter focuses on H-2 desorption from graphite (0001) in Temperature Programmed Desorption Monte Carlo simulations. The results are compared to experimental results which show two main peaks and an intermediate shoulder for high initial coverage. The simulation program includes barriers obtained by ab-initio methods and is further optimised to match two independent experimental observations. The simulations reproduce the two experimental observed desorption peaks. Additionally, a possible origin of the intermediate peak is given. (C) 2009 Elsevier B. V. All rights reserved.