  White dwarfs that have accreted planetary bodies are a powerful probe of the
bulk composition of exoplanetary material. In this paper, we present a Bayesian
model to explain the abundances observed in the atmospheres of 202 DZ white
dwarfs by considering the heating, geochemical differentiation, and collisional
processes experienced by the planetary bodies accreted, as well as
gravitational sinking. The majority (>60%) of systems are consistent with the
accretion of primitive material. We attribute the small spread in refractory
abundances observed to a similar spread in the initial planet-forming material,
as seen in the compositions of nearby stars. A range in Na abundances in the
pollutant material is attributed to a range in formation temperatures from
below 1,000K to higher than 1,400K, suggesting that pollutant material arrives
in white dwarf atmospheres from a variety of radial locations. We also find
that Solar System-like differentiation is common place in exo-planetary
systems. Extreme siderophile (Fe, Ni or Cr) abundances in 8 systems require the
accretion of a core-rich fragment of a larger differentiated body to at least a
3sigma significance, whilst one system shows evidence that it accreted a
crust-rich fragment. In systems where the abundances suggest that accretion has
finished (13/202), the total mass accreted can be calculated. The 13 systems
are estimated to have accreted masses ranging from the mass of the Moon to half
that of Vesta. Our analysis suggests that accretion continues for 11Myrs on
average.
