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We prove the arithemtic quantum unique ergodicity (AQUE) conjecture forsequences of Hecke--Maass forms on quotients $\Gamma\backslash(\mathbb{H}^{(2)})^r \times (\mathbb{H}^{(3)})^s$. An argument by induction ondimension of the orbit allows us to rule out the limit measure concentrating onclosed orbits of proper subgroups despite many returns of the Heckecorrespondence to neighborhoods of the orbit.

Arithmetic quantum unique ergodicity for products of hyperbolic $2$- and $3$-manifolds