Using a statistical model for the effects of decoherence , we show that in linear tight-binding samples ohmic conductance (resistance proportional to length) is reached for any finite density p of decoherence sites, if the chemical potential μ of the contacts is within a conducting band. If μ is outside a band, or if due to disorder, no bands form, for high decoherence densities p>p*
still ohmic conductance is reached, where p*
is a critical decoherence density. For p<p*
, the sample resistance increases exponentially with the length.