  A significant fraction of white dwarfs show metal lines indicative of
pollution with planetary material but the accretion process remains poorly
understood. The main aim of this paper is to produce a road-map illustrating
several potential routes for white dwarf pollution and to link these paths to
observational outcomes. Our proposed main road begins with the tidal disruption
of a scattered asteroid and the formation of a highly eccentric tidal disc with
a wide range of fragment sizes. Accretion of these fragments by
Poynting-Robertson (PR) drag alone is too slow to explain the observed rates.
Instead, in the second stage, several processes including differential apsidal
precession cause high-velocity collisions between the eccentric fragments.
Large asteroids produce more fragments when they disrupt, causing rapid
grind-down and generating short and intense bursts of dust production, whereas
smaller asteroids grind down over longer periods of time. In the final stage,
the collisionally produced dust circularises and accretes onto the white dwarf
via drag forces. We show that optically thin dust accretion by PR drag produces
large infrared (IR) excesses when the accretion rate exceeds 10^7 g/s. We
hypothesise that around white dwarfs accreting at a high rate, but with no
detected infrared excess, dust circularisation requires enhanced drag - for
instance due to the presence of gas near the disc's pericentre.
