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 ) \mathrm { M } _ { \odot } and ( 10 ^ { -9 } -10 ^ { -5 } ) { M _ { \odot } ~ { } yr ^ { -1 } } , respectively .
Thermal regimes in the parameters space \mathrm { 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 .