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We study the growth order of the maximal displacement of branching symmetric$\alpha$-stable processes. We assume the branching rate measure $\mu$ is in theKato class and $\mu$ has a compact support on ${\mathbb R}^d$. We show that themaximal displacement exponentially grows and its order is determined by theindex $\alpha$ and the spectral bottom of the corresponding Schr\"odinger-typeoperator.

Spread rate of catalytic branching symmetric stable processes