  We study the ultraviolet stability of gravity-matter systems for general
numbers of minimally coupled scalars and fermions. This is done within the
functional renormalisation group setup put forward in
\cite{Christiansen:2015rva} for pure gravity. It includes full dynamical
propagators and a genuine dynamical Newton's coupling, which is extracted from
the graviton three-point function.
  We find ultraviolet stability of general gravity-fermion systems.
Gravity-scalar systems are also found to be ultraviolet stable within validity
bounds for the chosen generic class of regulators, based on the size of the
anomalous dimension. Remarkably, the ultraviolet fixed points for the dynamical
couplings are found to be significantly different from those of their
associated background counterparts, once matter fields are included. In
summary, the asymptotic safety scenario does not put constraints on the matter
content of the theory within the validity bounds for the chosen generic class
of regulators.
