A list of n strings each of length n is being sorted in lexicographical order using the merge sort algorithm. Since we have to take care of comparison of each character in the strings so the merge step would be $O(n^2)$. So the recurrence should be of the form
$$T(n) = 2T(\frac n2) + O(n^2)$$
By master's theorem it solves to $O(n^2)$.
Somehow some people on the internet claim the following explanation: Merge sort makes $O(nlogn)$ comparisons and since it is lexicographical sort each comparison take $O(n)$ time, so worst case time is $O(n^2logn)$.
Which of the above is correct and if at some point i am incorrect please correct me.