  The evolution of the magnetic field of an accreting magnetic white dwarf with
an initially dipolar field at the surface has been studied for non-spherical
accretion under simplifying assumptions. Accretion on to the polar regions
tends to advect the field toward the stellar equator which is then buried. This
tendency is countered by Ohmic diffusion and magneto-hydrodynamic
instabilities. It is argued that if matter is accreted at a rate of
$\dot{M}_{\rm crit} \sim 10^{16}$ g s$^{-1}$ and the total mass accreted
exceeds a critical value $\Delta M_{\rm crit} \sim 0.1-0.2\ms$, the field may
be expected to be restructured, and the polar field to be reduced} reaching a
minimum value of $\sim 10^3$ G (the "bottom field") independently of the
initial field strength. Below this critical accretion rate, the field diffuses
faster than it can be advected, and accretion has little effect on field
strength and structure.
