  The structure of the general solution of the inhomogeneous evolution
equations allows the separation of a photon structure function into
perturbative (``anomalous") and non-perturbative contributions. The former part
is fully calculable, and can be identified with the high-mass contributions to
the dispersion integral in the photon mass. Properly normalized ``state"
distributions can be defined, where the $\gamma\to\qqbar$ splitting probability
is factored out. These state distributions are shown to be useful in the
description of the hadronic event properties, and necessary for a proper
eikonalization of jet cross sections. Convenient parametrizations are provided
both for the state and for the full anomalous parton distributions. The
non-perturbative parts of the parton distribution functions of the photon are
identified with the low-mass contributions to the dispersion integral. Their
normalizations, as well as the value of the scale $Q_0$ at which the
perturbative parts vanish, are fixed by approximating the low-mass
contributions by a discrete, finite sum of vector mesons. The shapes of these
hadronic distributions are fitted to the available data on $F_2^\gamma(x,Q^2)$.
Parametrizations are provided for $Q_0=0.6\,$GeV and $Q_0=2\,$GeV, both in the
DIS and the $\overline{\mathrm{MS}}$ factorization schemes. The full
parametrizations are extended towards virtual photons. Finally, the often-used
``FKP-plus-TPC/$2\gamma$" solution for $F_2^\gamma(x,Q^2)$ is commented upon.
