  There is growing evidence, based on both X-ray and radio observations of
isolated neutron stars, that besides the large--scale (dipolar) magnetic field,
which determines the pulsar spin--down behaviour, small--scale poloidal field
components are present, which have surface strengths one to two orders of
magnitude larger than the dipolar component. We argue in this paper that the
Hall--effect can be an efficient process in producing such small--scale field
structures just above the neutron star surface. It is shown that due to a
Hall--drift induced instability, poloidal magnetic field structures can be
generated from strong subsurface toroidal fields, which are the result of
either a dynamo or a thermoelectric instability acting at early times of a
neutron star's life. The geometrical structure of these small--scale surface
anomalies of the magnetic field resembles that of some types of
``star--spots''. The magnetic field strength and the length--scales are
comparable with values that can be derived from various observations.
