  The cross section for the inclusive photoproduction of large-p_T D^*+- mesons
is calculated at next-to-leading order, adopting different approaches to
describe the fragmentation of charm quarks into D^*+- mesons. We treat the
charm quark according to the massless factorization scheme, where it is assumed
to be one of the active flavours inside the proton and the photon. We present
inclusive single-particle distributions in transverse momentum and rapidity,
including the contributions due to both direct and resolved photons. We compare
and assess the various implementations of fragmentation. We argue that, in the
high-p_T regime, a particularly realistic description can be obtained by
convoluting the Altarelli-Parisi-evolved fragmentation functions of Peterson et
al. with the hard-scattering cross sections of massless partons where the
factorization of the collinear singularities associated with final-state charm
quarks is converted to the massive-charm scheme. The predictions thus obtained
agree well with recent experimental data by the H1 and ZEUS Collaborations at
DESY HERA.
