Diffusion and Drift Current under no biasing of a PN junction Diode In a PN diode, I get the point that total current is zero due to drift and diffusion current contribution cancels their effect when depletion region is formed.
My question is even though just for a moment suppose statistically electron in large amount diffused to p side and due to phenomena of recombination after some distance it will recombine. Then how does one say they constitute a current if they just diffuse by any means to p side, i.e. how does one say or calculate current or current flows if so they recombine with the holes.
If my question doesn't make you understand what i asked, so say in Forward biasing as diffusion will now easily takes place of majority charge carrier and we say a diffusion current is formed. But the majority carrier just simply recombines every time so what constitutes the diffusion current and how do we measure this current flowing in diode.
Also what is the role of battery in analyzing pn diode. Does it also provide extra electrons and they are the reason for current contribution or what.
Because in some text some says holes and electron are attracted by a battery and a current flows, which according to me is absurd.
 A: 
Then how does one say they constitute a current if they just diffuse by any means to p side

Movement of charge is electric current. This is moving charge, therefore it is current.
ANY movement of charge is current. If you put a bunch of electrons on a baseball and threw it across the field, that's an electric current. Its not a very constant current, but it is a current.
Unlike my baseball example, diffusion current in semiconductors is a very predictable process leading to a steady state current.

i.e. how does one say or calculate current or current flows if so they recombine with the holes

Just because the charges recombine after moving doesn't mean they weren't moving. They were moving and therefore were participating in current prior to recombination.
You can calculate diffusion current from the electron and hole gradient and the diffusivity of electrons and holes.

But the majority carrier just simply recombines every time so what constitutes the diffusion current and how do we measure this current flowing in diode.

Those carriers that diffuse over to the other side of the junction, become minority carriers, and recombine have to pair up with a majority charge carrier to do so. This majority carrier participating in the recombination has to be replaced in order to maintain charge neutrality in the semiconductor. This means while the diffusion current of the minority carriers decreases as they recombine, the total current remains constant because majority carriers begin to take over.
You can't measure it directly in a diode, you can only measure the net current. But the model is quite accurate with those measurements that we can do.
There are diffusion current measurements that can be done if you try hard enough. The Haynes-Shockley experiment is such an example
https://en.wikipedia.org/wiki/Haynes%E2%80%93Shockley_experiment
Using a laser to generate a carrier gradient without the presence of an electric field allowed them to measure diffusion current.

Also what is the role of battery in analyzing pn diode.

Don't think about how you get the external voltage, it is irrelevant. Just assume you can apply voltage to the p and n regions. It doesn't need to be a battery, in real life it probably is very rarely a battery anyway.

Does it also provide extra electrons and they are the reason for current contribution or what.

Your external voltage supply will provide a source of electrons to the n side of the junction to counteract those that leave from the p side.

Because in some text some says holes and electron are attracted by a battery and a current flows, which according to me is absurd.

Why is this absurd? Applying an electric field to charges applies a force to those charges and makes them want to move around. One of the most important properties of charge carriers (electrons and holes) is that they can move around, and so they do. This is exactly what happens in a resistor or even a wire.
