  In this paper we generalize the conformal limit correspondence between Higgs
bundles and holomorphic connections to the parabolic setting. Under mild
genericity assumptions on the parabolic weights, we prove that the conformal
limit always exists and that it defines holomorphic sections of the space of
parabolic lambda-connections which preserve a natural stratification and
foliate the moduli space. Along the way, we give a careful gauge theoretic
construction of the moduli space of parabolic Higgs bundles with full flags
which allows the eigenvalues of the residues of the Higgs field to vary. A
number of new phenomena arise in the parabolic setting. In particular, in the
generality we consider, unlike the nonparabolic case, the nonabelian Hodge
correspondence does not define sections of the space of logarithmic
lambda-connections, and the conformal limit does not define a one-parameter
family in any given moduli space.
