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This work provides compact representations for single- and multi-robot motion planning in the context of prehensile robot manipulation. This work explores asymptotic near-optimality and probabilistic near-optimality of these planners. This allows for lightweight storage of planning structures which are quick to query, and provides probabilistic bounds on path quality after finite computation. A compact representations for n-arm manipulation is given and efficient planning methods for multi-robot planning involving object hand-offs are provided. This work provides significant groundwork for asymptotically-optimal integrated task and motion planning for multi-arm manipulation.