  Black holes cannot support their own internal magnetic field like, for
example, compact stars can. Despite this fact observations indicate that event
horizons of supermassive black holes (SMBH) are threaded by field lines along
which plasma streams flow. Various magnetohydrodynamical mechanisms have been
suggested to generate turbulent magnetic fields on small scales, however, the
origin of the large-scale component is unclear. In this write-up we describe
our progress in an on-going work and discuss the possibility of dipole-type
magnetic fields being brought onto SMBH by magnetized neutron stars, which are
expected to drift inward from a hidden population in the Nuclear Star Cluster.
This can contribute to an organised component of the magnetic field on the
characteristic length-scale of the stellar size, which thread the horizon
during the final stages of the magnetized star plunge into or its close flyby
around SMBH. Because of mass--size scaling relations for black holes, the
effect is more important for lower-mass SMBH.
