  We examine the behaviour of an axisymmetric galactic dynamo model with a
radial accretion flow in the disc. We also introduce a vertical magnetic flux
through the galactic midplane, to simulate the presence of a large scale
magnetic field trapped by the galaxy when forming. The trapped vertical flux is
conserved and advected towards the disc centre by the radial flow. We confirm
that accretion flows of magnitude several km/s through a significant part of
the galactic disc can markedly inhibit dynamo action. Moreover, advection of
the vertical flux in general results in mixed parity galactic fields. However,
the effect is nonlinear and non-additive -- global magnetic field energies are
usually significantly smaller that the sum of purely dynamo generated and
purely advected field energies. For large inflow speeds, a form of
`semi-dynamo' action may occur.
  We apply our results to the accumulation and redistribution, by a radial
inflow, of a vertical magnetic flux captured by the Galactic disc. Taking
representative values, it appears difficult to obtain mean vertical fields near
the centre of the Milky Way that are much in excess of 10 microgauss, largely
because the galactic dynamo and turbulent magnetic diffusion modify the
external magnetic field before it can reach the disc centre.
