  We analyse, using new analytical models and numerical general relativistic
magnetohydrodynamic simulations, the three-dimensional properties of accretion
flows inside the plunging region of black hole spacetimes (i.e., at radii
smaller than the innermost stable circular orbit). These simulations are of
thick discs, with aspect ratios of order unity $h/r \sim 1$, and with a
magnetic field geometry given by the standard low-magnetization "SANE"
configuration. This work represents the first step in a wider analysis of this
highly relativistic region. We show that analytical expressions derived in the
"thin disc" limit describe the numerical results remarkably well, despite the
large aspect ratio of the flow. We further demonstrate that accretion within
this region is typically mediated via spiral arms, and that the geometric
properties of these spiral structures can be understood with a simple
analytical model. These results highlight how accretion within the plunging
region is fundamentally two dimensional in character, which may have a number
of observational implications. We derive a modified theoretical description of
the pressure within the plunging region which accounts for turbulent heating
and may be of use to black hole image modelling.
