Consider Merge-sort algorithm that we modify as follow:
Suppose we extend it to divide the input array into $m$ not necessary equal and after sorting each of them, merge them. Now can we conclude that the running time will be $O(n\log n)$?
I think the running time should be $O(n^2)$ as follow:
If the algorithm divide to three sections such that two first sections contains some constant number of elements and third sections contains all most elements then the running time will be $O(n^2)$ if the algorithm continue dividing as mentioned scenario.