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

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... urface. 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.