My basic idea of what a DC current is that, when a potential difference is applied to the ends of wire it creates a force which propagates through the wire all the way to the other end. It propagates in this way - Since the only mobile charges are electrons therefore positive part of the battery applies an EMF which pulls the nearby electrons from the wire connected to positive terminal and which subsequently leaves the blank positively charged site which is then filled by the nearby atom and so on. This happens throughout the wire, and at the end, near the negative terminal fresh electrons are supplied constantly. So in a current, blank positive sites are constantly created which then pulls the nearby electrons.
Now, my query is that - Is it necessary that the blank positive site created has the EMF equal to that of the battery at the end ? If so, why ? Will it not depend upon the amount of blank positive sites created at one point (in other words "concentration") which will eventually pull the electrons with more force ? What if the wire is very thin ?