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We study the problem of packing $k$ vertex-disjoint copies of $K_{1,r}$ ($k\\ge 2$) into a graph $G$ from parameterized preprocessing, i.e., kernelization, point of view. We show that every graph $G\\in {\\cal G}_d$ can be reduced, in polynomial time, to a graph $G'\\in {\\cal G}_d$ with $O(k)$ vertices such that $G$ has at least $k$ vertex-disjoint copies of $K_{1,r}$ if and only if $G'$ has. 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