Q: how can the current flow if the potential difference is 0 volts? I have read so many articles on so many websites about transistors and everywhere it says that when transistor is acting as a closed switch and conducting the voltage across collector-emitter is 0 volts, so how can the current flow if the applied voltage across two points is 0 volts?


A: This is one of those situations where "ideal model" and "real physical system" differ; all real physical conductors (except superconductors, which are weird) have ohmic properties and a non-zero resistance. So the voltage won't be zero, it'll be nearly zero.
Educational models and many simulators round "nearly zero" to zero to reduce clutter.

A: In reality the voltage difference will seldom be zero.  If the transistor is switched fully on then the voltage drop will be small (much less than 1 volt).  To say that it's zero is an over-simplification

A: If the voltage is zero and the resistance is zero then: -
$$\text{Current} = \dfrac{0}{0}$$
In other words, you cannot determine what current is flowing by simple ohm's law.
Think about a pure inductor; you apply a voltage across it and current ramps up at a rate of: -
$$\dfrac{V}{L} \hspace{1cm}\text{amps per second}$$
After a short time you disconnect the voltage and instantly apply a short across the pure inductor. Current continues to flow indefinitely. It's not magic.

everywhere it says that when transistor is acting as a closed switch
and conducting the voltage across collector-emitter is 0 volts

Everywhere you have read that is either incorrect or, you have misread that information because it's a physical impossibility.
