  We show how the Hopf algebra of rooted trees encodes the combinatorics of
Epstein-Glaser renormalization and coordinate space renormalization in general.
In particular we prove that the Epstein-Glaser time-ordered products can be
obtained from the Hopf algebra by suitable Feynman rules, mapping trees to
operator-valued distributions. Twisting the antipode with a renormalization map
formally solves the Epstein-Glaser recursion and provides local counterterms
due to the Hochschild 1-closedness of the grafting operator $B_+$.
