We extend the definition of tridendriform bialgebra by introducing a weight
q. The subspace of primitive elements of a q-tridendriform bialgebra is
equipped with an associative product and a natural structure of brace algebra,
related by a distributive law. This data is called q-Gerstenhaber-Voronov
algebras. We prove the equivalence between the categories of connected
q-tridendriform bialgebras and of q-Gerstenhaber-Voronov algebras.