we propose a polynomial self-stabilizing algorithm for maximal graph decomposition into p-
stars. Given an arbitrary graph G and a positive integer p⩾ 1, this decomposition provides
disjoint components of G, such that each component induces a p-star in G. Under the unfair
distributed scheduler, the algorithm converges within O (Δ 2 m) moves where m is the
number of edges and Δ is maximum node degree in the graph G.