  Rado's Conjecture is a compactness/reflection principle that says any
nonspecial tree of height $\omega_1$ has a nonspecial subtree of size $\leq
\aleph_1$. Though incompatible with Martin's Axiom, Rado's Conjecture turns out
to have many interesting consequences that are consequences of forcing axioms.
In this paper, we obtain consistency results concerning Rado's Conjecture and
its Baire version. In particular, we show a fragment of PFA, that is the
forcing axiom for \emph{Baire Indestructibly proper forcings}, is compatible
with the Baire Rado's Conjecture. As a corollary, Baire Rado's Conjecture does
not imply Rado's Conjecture. Then we discuss the strength and limitations of
the Baire Rado's Conjecture regarding its interaction with simultaneous
stationary reflection and some families of weak square principles. Finally we
investigate the influence of the Rado's Conjecture on some polarized partition
relations.
