  (Abridged) We present the results of the first unbiased survey for metal
pollution among H-atmosphere (DA) white dwarfs with cooling ages of 20-200 Myr
and 17000K < Teff < 27000K, using HST COS in the far UV between 1130 and 1435
A. The atmospheric parameters and element abundances are determined using
theoretical models, which include the effects of element stratification due to
gravitational settling and radiative levitation.
  We find 48 of the 85 DA white dwarfs studied, or 56% show traces of metals.
In 25 stars, the elements can be explained by radiative levitation alone,
although we argue that accretion has very likely occurred recently. The
remaining 23 white dwarfs (27%) must be currently accreting. Together with
previous studies, we find no accretion rate trend in cooling age from ~40 Myr
to ~2 Gyr. The median, main sequence progenitor of our sample corresponds to a
star of ~2 Msun, and we find 13 of 23 white dwarfs descending from 2-3 Msun
late B- and A-type stars to be currently accreting. Only one of 14 targets with
Mwd > 0.8 Msun is found to be currently accreting, which suggests a large
fraction are double-degenerate mergers, and the merger discs do not commonly
reform large planetesimals or otherwise pollute the remnant. We reconfirm our
previous finding that two white dwarf Hyads are currently accreting rocky
debris.
  At least 27%, and possibly up to ~50%, of all white dwarfs with cooling ages
20-200 Myr are accreting planetary debris. At Teff > 23000K, the luminosity of
white dwarfs is likely sufficient to vaporize circumstellar dust, and hence no
stars with strong metal-pollution are found. However, planetesimal disruption
events should occur in this cooling age and Teff range as well, and likely
result in short phases of high mass transfer rates. It appears that the
formation of rocky planetary material is common around 2-3 Msun late B- and
A-type stars.
