  We present full evolutionary calculations appropriate for the study of hot
hydrogen-deficent DO white dwarfs, PG 1159 stars, and DB white dwarfs. White
dwarf sequences are computed for a wide range of stellar masses and helium
envelopes on the basis of a complete treatment of the evolutionary history of
progenitors stars, including the core hydrogen and helium burning phases, the
thermally-pulsing AGB phase, and the born-again episode that is responsible for
the hydrogen deficiency. We also provide colors and magnitudes for the new
sequences for $T_{\rm eff} < 40 000$ K, where the NLTE effects are not
dominant. These new calculations provide an homogeneous set of evolutionary
tracks appropriate for mass and age determinations for both PG 1159 stars and
DO white dwarfs. The calculations are extended down to an effective temperature
of 7 000 K. We applied these new tracks to redetermine stellar masses and ages
of all known DO white dwarfs with spectroscopically-determined effective
temperatures and gravities, and compare them with previous results. We also
compare for the first time consistent mass determinations for both DO and PG
1159 stars, and find a considerably higher mean mass for the DO white dwarfs.
We discuss as well the chemical profile expected in the envelope of variable DB
white dwarfs from the consideration of the evolutionary history of progenitor
stars. Finally, we present tentative evidence for a different evolutionary
channel, other than that involving the PG 1159 stars, for the formation of hot,
hydrogen-deficient white dwarfs.
