just wanted to find out under what scenario an aircraft would veer off a runway due to differential friction/ i guess u guys do not know that
This would be something (I would have thought) that would be evaluated (or would have, years ago) by the a/c manufacturer and certification authorities, in general terms. Based on a broad spectrum of analysis and tests, limits, issues and a general understanding would have been developed. This would be carried over to new a/c design, using scaling/modelling of some sort - 'if' it was likely to be an issue.
It could well be that, due to mass and inertia considerations, it is a 'least significant' issue until the a/c has slowed considerably.
There are (at least) two distinct phases during landing, as far as kinematic antics are concerned - above and below the speeds at which aerodynamic forces predominate over runway frictional forces. Although as ever, there are many grey areas no doubt... where combinations can have profound influence.
In short, there are probably few if any 'strict' criteria on acceptable runway yaw angles, and if there are, it would be more likely structural load considerations than 'controllability' issues that were at the root of any such figures.
You can thus hopefully now accept, that specifying a single kinematic criteria when probably a dozen are involved, is considered a little naive especially when this sort of behaviour is way and above what a pilot is concerned with - if the show gets well out of line at some point, all one can normally do is use what aerodynamic, steering and braking corrections are available at the speed and conditions one finds oneself in.