  The results of a NLTE model atmosphere analysis of 27 hydrogen-rich central
stars of old planetary nebulae (PN) are reported. These stars were selected
from a previous paper in this series, where we gave classifications for a total
of 38 central stars. Most of the analyzed central stars fill a previously
reported gap in the hydrogen-rich evolutionary sequence. Our observations imply
the existence of two separated spectral evolutionary sequences for
hydrogen-rich and -poor central stars/white dwarfs. This is in line with
theoretical evolutionary calculations, which predict that most post-AGB stars
reach the white dwarf domain with a thick hydrogen envelope of approx. 10^-4
Msun.
  We determine stellar masses from the comparison with evolutionary tracks and
derive a mass distribution for the hydrogen-rich central stars of old PNe. The
peak mass and the general shape of the distribution is in agreement with recent
determinations of the white dwarf mass distribution. The properties of most
analyzed stars are well explained by standard post-AGB evolution. However, for
eight stars of the sample other scenarios have to be invoked.
  A wide spread of helium abundances is observed in the photospheres of central
stars of old PNe. It is shown that a good correlation between helium abundances
and luminosity is present. It is inferred that when the stars' luminosities
fall below L = 300Lsun depletion starts and the helium abundance steadily
decreases with decreasing luminosity. The existence of this correlation is in
qualitative agreement with recent theoretical calculations of gravitational
settling in the presence of a stellar wind.
