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We present a silent self-stabilizing distributed algorithm computing a maximal |$\ p$| -star decomposition of the underlying communication network. Under the unfair distributed scheduler, the most general scheduler model, the algorithm converges in at most |$12\Delta m + \mathcal{O}(m+n)$| moves, where |$m$| is the number of edges, |$n$| is the number of nodes and |$\Delta $| is the maximum node degree. Regarding the time complexity, we obtain the following results: our algorithm outperforms the previously known best algorithm by a factor of |$\Delta $| with respect to the move complexity. While the round complexity for the previous algorithm was unknown, we show a |$5\big \lfloor \frac{n}{p+1} \big \rfloor +5$| bound for our algorithm. [ABSTRACT FROM AUTHOR]