  We theoretically investigate the magnetic flux transport in geometrically
thick accretion discs which may form around black holes. We utilize a
two-dimensional (2D) kinematic mean-field model for poloidal field transport
which is governed by both inward advection and outward diffusion of the field.
Assuming a steady state, we analytically show that the multi-dimensional
effects prevent the field accumulation toward the centre and reduce the field
inclination angle. We also numerically investigate the radial profile of the
field strength and the inclination angle for two geometrically thick discs for
which (quasi-)analytic solutions exist: radiatively inefficient accretion flows
(RIAFs) and super-Eddington accretion flows. We develop a 2D kinematic
mean-field code and perform simulations of flux transport to study the
multi-dimensional effects. The numerical simulations are consistent with our
analytical prediction. We also discuss a condition for the external field
strength that RIAF can be a magnetically arrested disc. This study could be
important for understanding the origin of a large-scale magnetic field that
drives jets and disc winds around black holes.
