Given a discrete subgroup G ⊂ PSL(3, C), acting on the complex projective plane, P2C , in the canonical way, we list all possible values for the number of complex projective lines and for the maximum number of complex projective lines lying in the complement of each of: the equicontinuity set of G, the Kulkarni discontinuity region of G, and maximal open subsets of P2C on which G acts properly discontinuously.