We clarify the relation between noncommutative Poisson boundaries and Furstenberg–Hamana of quantum groups. Specifically, given a compact group G, we show that in many cases where boundary dual discrete Gˆ has been computed, underlying topological either coincides with Drinfeld double D(G) G or is quotient it. This includes q-deformations Lie groups, free orthogonal unitary automorphism groups ...