This paper introduces a new problem extended maximal P -star partition where maximal　p-star decompositions are concurrently constructed for p = 0, 1, . . . , P for a given P . We　propose a self-stabilizing algorithm constructing the extended maximal P -star partition of a　distributed network. The extended maximal P -star partition is a partition of nodes in a graph　such that for any p (≤ P ), maximal p-star decomposition is constructed for a graph excluding　nodes belonging to larger stars. Under the unfair distributed daemon, the most general　scheduler model, our proposed algorithm converges in at most O(n) rounds with O(P log n)
space per process, where n is the number of nodes. Though the extended maximal P -star　partition is achieved with a fair composition of maximal p-star decomposition algorithms for　p = 0, 1, . . . , P , the proposed algorithm only requires the same space complexity as existing　maximal P -star decompoition, that concludes, it drastically reduces space complexity with　comparable round complexity compared to a fair composition of existing algorithms.