Re: bjt
I believe there is a small misconception here.
As a first order approximation, in the cut off region Ic=Ib=Ie=0.
i.e. there is no current in the emitter branch
If we want a second order analysis, there is a small leakage current in the BJT during cut off, just like the reverse leakage current in the diode in the presence of non-zero voltage accross its terminals.
In the large signal model, we assume there is a leakage current through the emitter-base and collegector base junctions, but these currents are very small to be of practcal interest. (nA->pA's)