  We show that the effective field equations for a recently formulated
polynomial affine model of gravity, in the sector of a torsion-free connection,
accept general Einstein manifolds---with or without cosmological constant---as
solutions. Moreover, the effective field equations are partially those obtained
from a gravitational Yang--Mills theory known as Stephenson--Kilmister--Yang
theory. Additionally, we find a generalization of a minimally coupled massless
scalar field in General Relativity within a "minimally" coupled scalar field in
this affine model. Finally, we present a brief analysis of the propagators of
the gravitational theory, and count the degrees of freedom. For completeness we
prove that a Birkhoff-like theorem is valid for the analyzed sector.
