  We consider an electron with an anomalous magnetic moment g>2 confined to a
plane and interacting with a nonzero magnetic field B perpendicular to the
plane. We show that if B has compact support and the magnetic flux in the
natural units is F\ge 0, the corresponding Pauli Hamiltonian has at least 1+[F]
bound states, without making any assumptions about the field profile.
Furthermore, in the zero-flux case there is a pair of bound states with
opposite spin orientations. Using a Birman-Schwinger technique, we extend the
last claim to a weak rotationally symmetric field with B(r) = O(r^{-2-\delta})
correcting thus a recent result. Finally, we show that under mild regularity
assumptions the existence can be proved for non-symmetric fields with tails as
well.
