  Photoionization models of HII regions require as input a description of the
ionizing SED and of the gas distribution, in terms of ionization parameter U
and chemical abundances (e.g. O/H and N/O). A strong degeneracy exists between
the hardness of the SED and U, which in turn leads to high uncertainties in the
determination of the other parameters, including abundances. One way to resolve
the degeneracy is to fix one of the parameters using additional information.
  For each of the ~ 20000 sources of the CALIFA HII regions catalog, a grid of
photoionization models is computed assuming the ionizing SED being described by
the underlying stellar population obtained from spectral synthesis modeling.
The ionizing SED is then defined as the sum of various stellar bursts of
different ages and metallicities. This solves the degeneracy between the shape
of the ionizing SED and U. The nebular metallicity (associated to O/H) is
defined using the classical strong line method O3N2 (which gives to our models
the status of "hybrids"). The remaining free parameters are the abundance ratio
N/O and the ionization parameter U, which are determined by looking for the
model fitting [NII]/Ha and [OIII]/Hb. The models are also selected to fit
[OII]/Hb. This process leads to a set of ~ 3200 models that reproduce
simultaneously the three observations.
  We find that the regions associated to young stellar bursts suffer leaking of
the ionizing photons, the proportion of escaping photons having a median of
80\%. The set of photoionization models satisfactorily reproduces the electron
temperature derived from the [OIII]4363/5007 line ratio. We determine new
relations between the ionization parameter U and the [OII]/[OIII] or
[SII]/[SIII] line ratios. New relations between N/O and O/H and between U and
O/H are also determined.
  All the models are publicly available on the 3MdB database.
