no of times partion is called in quick sort, assuming array is always halved
The number of times the partition algorithm is called does not actually depend on where the array is partitioned (asymptotically).
To count the number of partitions you just need to count the number of internal nodes in the recursion tree. Since each internal node has at least two children, the recursion tree is a full binary tree. In a full binary tree, the number of leaves and internal nodes are linearly related (see this link). So the number of internal nodes would be $\Theta(n)$, no matter where the partition happens. You can easily prove this using induction on the number of nodes in the tree.