offset in measuring decomposition potentials as far as I've understood to measure the decomposition potential of an electrolyte using a galvanic cell we just put two electrodes, connect them to a battery, and vary the external potential till when we observe a current. The potential at which the current starts to grow linearly is the decomposition potential of the electrolyte. There is not appreciable current before the decompositon potential because the electrodes are supposed to be inert and do not provide the ionic charges needed to "close the circuit". Is it right? 
An other question. How the role of the electrodes is taken into consideration in the experimental setup? Is it considered an offset due to an eventual nonzero cell potential? I made this question because I'd like to be sure that I'm understanding the experimental setup.

Tirrel
Ok I will answer your  last question first. If you have two identical electrodes(i.e. same electrode material), the cell potential will be zero and there won't be any issues there.

You have to use inert electrodes so that you are not measuring the dissolution of the electrode itself.

The one part I am not sure you understand properly is the current growing. You want to vary the potential until the current raises exponentially when continuing to sweep. This will be a very sharp rise that will be hard to miss.