  The renormalization group flow of unimodular quantum gravity is investigated
within two different classes of truncations of the flowing effective action. In
particular, we search for non-trivial fixed-point solutions for polynomial
expansions of the $f(R)$-type as well as of the
$F(R_{\mu\nu}R^{\mu\nu})+R\,Z(R_{\mu\nu}R^{\mu\nu})$ family on a maximally
symmetric background. We close the system of beta functions of the
gravitational couplings with anomalous dimensions of the graviton and
Faddeev-Popov ghosts treated according to two independent prescriptions: one
based on the so-called background approximation and the other based on a hybrid
approach which combines the background approximation with simultaneous vertex
and derivative expansions. For consistency, in the background approximation, we
employ a background-dependent correction to the flow equation which arises from
the proper treatment of the functional measure of the unimodular path integral.
We also investigate how different canonical choices of the endomorphism
parameter in the regulator function affect the fixed-point structure. Although
we have found evidence for the existence of a non-trivial fixed point for the
two classes of polynomial projections, the $f(R)$ truncation exhibited better
(apparent) convergence properties. Furthermore, we consider the inclusion of
matter fields without self-interactions minimally coupled to the unimodular
gravitational action and we find evidence for compatibility of asymptotically
safe unimodular quantum gravity with the field content of the Standard Model
and some of its common extensions.
