It is known that the ranks of the semigroups

,

and

(the semigroups of orientation preserving singular self-maps, partial and strictly partial transformations on

, respectively) are n, 2n and n + 1, respectively. The idempotent rank, defined as the smallest number of idempotent generating set, of

and

are the same value as the rank, respectively. Idempotent can be seen as a special case (with m = 1) of m-potent. In this paper, we investigate the m-potent ranks, defined as the smallest number of m-potent generating set, of the semigroups

,

and

. Firstly, we characterize the structure of the minimal generating sets of

. As applications, we obtain that the number of distinct minimal generating sets is

. Secondly, we show that, for

, the m-potent ranks of the semigroups

and

are also n and 2n, respectively. Finally, we find that the 2-potent rank of

is n + 1.