  We investigate the smoothing problem of limit linear series of rank one on an
enrichment of the notions of nodal curves and metrized complexes called
saturated metrized complexes. We give a finitely verifiable full criterion for
smoothability of a limit linear series of rank one on saturared metrized
complexes, characterize the space of all such smoothings, and extend the
criterion to metrized complexes. As applications, we prove that all limit
linear series of rank one are smoothable on saturated metrized complexes
corresponding to curves of compact-type, and prove an analogue for saturated
metrized complexes of a theorem of Harris and Mumford on the characterization
of nodal curves contained in a given gonality stratum. In addition, we give a
full combinatorial criterion for smoothable limit linear series of rank one on
saturated metrized complexes corresponding to nodal curves whose dual graphs
are made of separate loops.
