  This paper is devoted to the global analysis of the three-dimensional
axisymmetric Navier--Stokes--Maxwell equations. More precisely, we are able to
prove that, for large values of the speed of light $c\in (c_0, \infty)$, for
some threshold $c_0>0$ depending only on the initial data, the system in
question admits a unique global solution. The ensuing bounds on the solutions
are uniform with respect to the speed of light, which allows us to study the
singular regime $c\rightarrow \infty$ and rigorously derive the limiting
viscous magnetohydrodynamic (MHD) system in the axisymmetric setting.
  The strategy of our proofs draws insight from recent results on the
two-dimensional incompressible Euler--Maxwell system to exploit the
dissipative--dispersive structure of Maxwell's system in the axisymmetric
setting. Furthermore, a detailed analysis of the asymptotic regime $c\to\infty$
allows us to derive a robust nonlinear energy estimate which holds uniformly in
$c$. As a byproduct of such refined uniform estimates, we are able to describe
the global strong convergence of solutions toward the MHD system.
  This collection of results seemingly establishes the first available global
well-posedness of three-dimensional viscous plasmas, where the electric and
magnetic fields are governed by the complete Maxwell equations, for large
initial data as $c\to\infty$.
