H-removable sequences, for arbitrary H, under &Lambda^* construction are presented here. In the first part we investigate Neighborhood Distinct (ND) graphs and ask some natural questions concerning disconnected H and H complement. In the second part, we introduce property * and investigate graphs that satisfy property *. Consequently we find $H$-removable sequences for all graphs H with up to 6 vertices except for G60. G60 is the only graph with up to 6 vertices for which neither it nor its complement satisfies property *. The last part of our work focuses on good and bad copies of arbitrary graphs $H$ and how to interchange from one to the other. The number of ways to count all possible copies of H in H_{pn} ^ &Lambda^* is also presented via examples.