Consider an electric circuit with a battery and a resistor connected through a wire of zero resistance. Since the wire offers no resistance, all points on the wire are at same potential, then why on earth does the electrons flow towards the resistor? And what if there was no resistor at all. Why would a potential difference arise in such a case? What would be the source of potential drop in this case?
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Firstly, any system attempts to achieve a state with minimal energy. So, for example, when the two plates of a parallel plate capacitor are connected, regardless of the resistance of the conductor used to connect the plates, current flows till both plates are natural.
The above explanation should answer "why the electrons move towards the conductor".
Now, I believe your questions lies in how the current is set up in the first place. I am of course assuming you are talking about superconductors here.
A factor you have to take into account is that conductors have properties other than resistance. For superconductors, the dominant property is inductance which controls current. Standard Ohm's law does not apply here as the resistance is zero.
For reference, check out Is current in superconductors infinite? If they have 0 resistance then I (V/R) should be infinite? which sort of is related to your question and also, read up on superconductivity https://en.wikipedia.org/wiki/Superconductivity.
Paddy
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