  Extended decorations on naturally decorated trees were introduced in the work
of Bruned, Hairer and Zambotti on algebraic renormalization of regularity
structures to provide a convenient framework for the renormalization of systems
of singular stochastic PDEs within that setting. This non-dynamical feature of
the trees complicated the analysis of the dynamical counterpart of the
renormalization process. We provide a new proof of the renormalized system
by-passing the use of extended decorations and working for a large class of
renormalization maps, with the BPHZ renormalization as a special case. The
proof reveals important algebraic properties connected to preparation maps.
