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The structure of the general solution of the inhomogeneous evolutionequations allows the separation of a photon structure function intoperturbative (``anomalous") and non-perturbative contributions. The former partis fully calculable, and can be identified with the high-mass contributions tothe dispersion integral in the photon mass. Properly normalized ``state"distributions can be defined, where the $\gamma\to\qqbar$ splitting probabilityis factored out. These state distributions are shown to be useful in thedescription of the hadronic event properties, and necessary for a propereikonalization of jet cross sections. Convenient parametrizations are providedboth for the state and for the full anomalous parton distributions. Thenon-perturbative parts of the parton distribution functions of the photon areidentified with the low-mass contributions to the dispersion integral. Theirnormalizations, as well as the value of the scale $Q_0$ at which theperturbative parts vanish, are fixed by approximating the low-masscontributions by a discrete, finite sum of vector mesons. The shapes of thesehadronic 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 theDIS and the $\overline{\mathrm{MS}}$ factorization schemes. The fullparametrizations 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.Comment: 33 pages, Latex, 6 Z-compressed and uuencoded figure

Low- and high-mass components of the photon distribution functions