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 $Delta M_{rm crit} sim 0.1-0.2ms$, 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.
