  Typed decorated trees are used by Bruned, Hairer and Zambotti to give a
description of a renormalisation processon stochastic PDEs. We here study the
algebraic structures on these objects: multiple prelie algebrasand related
operads (generalizing a result by Chapoton and Livernet), noncommutative and
cocommutative Hopf algebras (generalizing Grossman and Larson's
construction),commutative and noncocommutative Hopf algebras (generalizing
Connes and Kreimer's construction),bialgebras in cointeraction (generalizing
Calaque, Ebrahimi-Fard and Manchon's result). We also define families of
morphisms and in particular we prove that any Connes-Kreimer Hopf algebraof
typed and decorated trees is isomorphic to a Connes-Kreimer Hopf algebra of
non--typed and decoratedtrees (the set of decorations of vertices being
bigger), through a contraction process,and finally obtain the
Bruned-Hairer-Zambotti construction as a subquotient.
