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Unambiguous automata are usually seen as a natural class of automata in-between deterministic and nondeterministic ones. We show that in case of infinite tree languages, the unambiguous ones are topologically far more complicated than the deterministic ones. We do so by providing operations that generate a family A b α α<ϕ 2 (0) of unambiguous automata such that: 1. It respects the strict Wadge ordering: α < β if and only if A b α < W A b β. This can be established without the help of anyfatcat:hc4y2fqtgfcmbit2ey6lqgckeu