  We study Hom-type analogs of Rota-Baxter and dendriform algebras, called
Rota-Baxter $G$-Hom-associative algebras and Hom-dendriform algebras. Several
construction results are proved. Free algebras for these objects are explicitly
constructed. Various functors between these categories, as well as an
adjunction between the categories of Rota-Baxter Hom-associative algebras and
of Hom-(tri)dendriform algebras, are constructed.
