We present an explicit evidence, in the framework of 2-D MHD, of the existence of a stat in which energy is dissipated at a rate independent of the ohmic resistivity, thus proving the validity of a conjecture put forward more than twenty years ago, Matthaeus and Montgomery 1980. We also show that the time necessary to establish such a state is resistivity independent as well. The influence of the boundary conditions for achieving such conditions and the relevance of these results for the problem of coronal heating is discussed.