  The remarkable results by the Event Horizon Telescope collaboration
concerning the emission from M87* and, more recently, its polarization
properties, require an increasingly accurate modeling of the plasma flows
around the accreting black hole. Radiatively inefficient sources such as M87*
and Sgr A* are typically modeled with the SANE (standard and normal evolution)
paradigm, if the accretion dynamics is smooth, or with the MAD (magnetically
arrested disk) paradigm, if the black hole's magnetosphere reacts by halting
the accretion sporadically, resulting in a highly dynamical process. While the
recent polarization studies seem to favor MAD models, this may not be true for
all sources, and SANE accretion surely still deserves attention. In this work,
we investigate the possibility of reaching the typical degree of magnetization
and other accretion properties expected for SANE disks by resorting to the
mean-field dynamo process in axisymmetric GRMHD simulations, which are supposed
to mimic the amplifying action of an unresolved magnetorotational
instability-driven turbulence. We show that it is possible to reproduce the
main diagnostics present in the literature by starting from very unfavorable
initial configurations, such as a purely toroidal magnetic field with
negligible magnetization.
