It's known 2-way Merge sort takes N*logN time.
I wonder, what would be the running time if we split an array of the size N into N subarrays and then do the same thing as we would do for 2-way Merge?
Well, the recurrence will be:
Of course in 2-way merge sort we can do this in linear time, hence
Now, according to the Master Theorem you can solve this recurrence and see that
So in asymptotic notation it looks like both k-way and the original merge-sort are equal. however note that in practice, implementing the original merge-sort is simpler and might require less effort to implement and maintain.