  Let $F,G$ be bicomonads on a monoidal category $\mathcal{C}$. The aim of this
paper is to discuss the smash coproducts of $F$ and $G$. As an application, the
smash coproduct of Hom-bialgebras is discussed. Further, the Hom-entwining
structure and Hom-entwined modules are investigated.
