  We investigate experimentally the electric transport at the insulating side
of the superconductor to insulator transition in thin TiN-films. At
temperatures T > 50 mK we observe an Arrhenius-type conductance, with an
activation energy depending logarithmically on the sample size. At high bias
the current voltage (I-V) characteristics display a large current jump into an
electron heating dominated regime. For the largest samples, and below 50 mK we
observe a low-bias power law I ~ V^alpha characteristics with an exponent alpha
> 1 rapidly growing with decreasing temperature, which is expected for a
binding-unbinding crossover of the charge-Berezinskii-Kosterlitz-Thouless type.
