We present a detailed spectroscopic analysis of the stars with helium-dominated spectra in the ESO Supernova Ia Progenitor Survey (SPY). Atmospheric parameters, masses, and abundances of trace hydrogen are determined and discussed in the context of spectral evolution of white dwarfs. Our final sample contains 71 objects, of which 6 are new detections and 14 are reclassified from DB to DBA because of the presence of H lines. 55% of the DB sample show hydrogen and are thus DBA, a significantly higher fraction than found before. The large incidence of DBA, and the derived total hydrogen masses are compatible with the scenario that DBs ``reappear around 30000 K from the DB gap by mixing and diluting a thin hydrogen layer of the order of E-15 Msun. This hydrogen mass is then during the evolution continuously increased by interstellar accretion. There are indications that the accretion rate increases smoothly with age or decreasing temperature, a trend which continuous even below the current low temperature limit (Dufour 2006). A remaining mystery is the low accretion rate of H compared to that of Ca observed in the DBZA, but a stellar wind extending down to the lowest temperatures with decreasing strength might be part of the solution.
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