  The most general admissible boundary conditions are derived for an idealised
Aharonov-Bohm flux intersecting the plane at the origin on the background of a
homogeneous magnetic field. A standard technique based on self-adjoint
extensions yields a four-parameter family of boundary conditions; other two
parameters of the model are the Aharonov-Bohm flux and the homogeneous magnetic
field. The generalised boundary conditions may be regarded as a combination of
the Aharonov-Bohm effect with a point interaction. Spectral properties of the
derived Hamiltonians are studied in detail.
