I'm comparatively new to algorithm analysis and am taking a related course on coursera where I came accross k way merge sort. The time complexity of 2 way merge sort is n log2 n, of 3 way merge sort is n log3 n and of 4 way merge sort is n log4 n. But, in the case of k-way the complexity is nk^2. This is because we pay attention to the merge part of the algo; (2n + 3n + 4n...kn). But, in case of 2, 3 and 4-way algorithms, we pay attention to the recursive call of one function; (2T(n/2) + c.n).Can anybody please explain why this is so? Or correct my approach to this question.  
Why is time complexity of k-way merge sort O(nk^2)?
algorithms;sorting