  The behaviour of carbon-oxygen white dwarfs (WDs) subject to direct helium
accretion is extensively studied. We aim to analyze the thermal response of the
accreting WD to mass deposition at different time scales. The analysis has been
performed for initial WDs masses and accretion rates in the range (0.60 - 1.02)
Msun and 1.e-9 - 1.e-5 Msun/yr, respectively. Thermal regimes in the parameters
space M_{WD} - dot{M}_{He}, leading to formation of red-giant-like structure,
steady burning of He, mild, strong and dynamical flashes have been identified
and the transition between those regimes has been studied in detail. In
particular, the physical properties of WDs experiencing the He-flash accretion
regime have been investigated in order to determine the mass retention
efficiency as a function of the accretor total mass and accretion rate. We also
discuss to what extent the building-up of a He-rich layer via H-burning could
be described according to the behaviour of models accreting He-rich matter
directly. Polynomial fits to the obtained results are provided for use in
binary population synthesis computations. Several applications for close binary
systems with He-rich donors and CO WD accretors are considered and the
relevance of the results for the interpretation of He-novae is discussed.
