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The spatial structure of a class of superprocesses which arise as limits in distribution of a class of interacting particle systems with location dependent branching is investigated. The criterion of their state classification is obtained. Their effective state space is contained in the set of purely-atomic measures or the set of absolutely continuous measures according as one diffusive coefficient c(x) ≡ 0 or |c(x)| ≥ ε > 0 while another diffusive coefficient h ∈ C 2 b (R). 157doi:10.1214/ecp.v7-1057 fatcat:j76ntcps3feebfw547lkvi5hhy