  We have calculated the next-to-leading order cross section for the inclusive
production of charm quarks as a function of the transverse momentum p_T and the
rapidity in two approaches using massive or massless charm quarks. For the
single-resolved cross section we have derived the massless limit from the
massive theory. We find that this limit differs from the genuine massless
version with MS-bar factorization by finite corrections. By adjusting
subtraction terms we establish a massive theory with MS-bar subtraction which
approaches the massless theory very fast with increasing transverse momentum.
With these results and including the equivalent results for the direct cross
section obtained previously as well as double-resolved contributions, we
calculate the inclusive D*+- cross section in gamma-gamma collisions using
realistic evolved non-perturbative fragmentation functions and compare with
recent data from the LEP collaborations ALEPH, L3 and OPAL. We find good
agreement.
