We extend in this paper the concept of the P-admissible floorplan representation to that of the P*-admissible one. A P*-admissible representation can model the most general floorplans. Each of the currently existing P*-admissible representations, SP, BSG, and TCG, has its strengths as well as weaknesses. We show the equivalence of the two most promising P*-admissible representations, TCG and SP, and integrate TCG with a packing sequence (part of SP) into a new representation, called TCGS. TCG-S combines the advantages of SP and TCG and at the same time eliminates their disadvantages. With the property of SP, faster packing and perturbation schemes are possible. Inherited nice properties from TCG, the geometric relations among modules are transparent to TCGS (implying faster convergence to a desired solution), placement with position constraints becomes much easier, and incremental update for cost evaluation can be realized. These nice properties make TCG-S a superior representation wh...