  After briefly reviewing the results about polytropic stars in Palatini
f(R)-theories, we first show how these results rely on the assumption of a
regular function f(R). In particular, singular models allow to extend the
parameter interval in which no singularity is formed. Furthermore, we present
how the conformal metric can be matched smoothly in the cases where the
original metric generates a singularity. In fact, the singularity comes from a
singular conformal factor which is continuous though not differentiable at the
stellar surface. This suggests that the correct metric to be considered as
physical is the conformal metric. This is relevant because, even also when
matching the original metric is possible, the use of the conformal metric
generates different stellar models.
