  In this paper we describe the right-sided combinatorial Hopf structure of
three Hopf algebras appearing in the context of renormalization in quantum
field theory: the non-commutative version of the Fa\`a di Bruno Hopf algebra,
the non-commutative version of the charge renormalization Hopf algebra on
planar binary trees for quantum electrodynamics, and the non-commutative
version of the Pinter renormalization Hopf algebra on any bosonic field. We
also describe two general ways to define the associative product in such Hopf
algebras, the first one by recursion, and the second one by grafting and
shuffling some decorated rooted trees.
