We present results demonstrating the effect of varying microchannel depth and bulk conductivity on the space charge-mediated transition between classical, diffusion-limited current and over-limiting current in microchannel-nanochannel devices. The extended space charge layer develops at the depleted microchannel-nanochannel entrance when the limiting current is exceeded and is correlated with a distinctive maximum in the dc resistance. This maximum is shown to be affected by the microchannel depth, via field-focusing, and solution conductivity. In particular, we observe that upon their increase, the maximum becomes flatter and shifts to higher voltages.