  Protoplanetary discs (PPDs) are cold, dense and weakly ionised environments
that witness the planetary formation. Among these discs, transition discs (TDs)
are characterised by a wide cavity in the dust and gas distribution. Despite
this lack of material, many TDs strongly accrete onto their central star,
possibly indicating that a mechanism is driving fast accretion in TDs cavities.
The presence of radially extended 'dead zones' in PPDs recently revived the
interest in magnetised disc winds (MDWs), where accretion is driven by a large
magnetic field. We propose that TDs could be subject to similar winds,
explaining their fast-accreting and long-lived cavities. We present the results
of the first 2.5D global numerical simulations of TDs harbouring MDWs using the
PLUTO code. We impose a cavity in the gas distribution and consider a power law
distribution for the large-scale magnetic field strength. We assume weakly
ionised discs subject to ambipolar diffusion, as expected in this range of
densities and temperatures. Our simulated TDs reach a steady state with an
inner cavity and an outer 'standard' disc. The accretion rates remain
approximately constant through the entire discs, reaching
$10^{-7}~M_\odot/\text{yrs}^{-1}$ for typical surface density values. The MDW
launched from the cavity is more magnetised with a much larger lever arm than
the MDW launched from the outer disc. The material in the cavity is accreted at
sonic velocities, and the cavity itself is rotating at 70% of the Keplerian
velocity due to the efficient magnetic braking imposed by the MDW. Overall, our
cavity matches the dynamical properties of an inner jet emitting disc (JED) and
of magnetically arrested discs (MADs) in black hole physics. Finally, kinematic
diagnostics (wind speeds, orbital and accretion velocities) could disentangle
classical photo-evaporation from MDW models.
