  We illuminate effects of surface-charge convection intrinsic to
leaky-dielectric electrohydrodynamics by analyzing the symmetric steady state
of a circular drop in an external field at arbitrary electric Reynolds number
$\mathrm{Re}_E$. In formulating the problem, we identify an exact factorization
that reduces the number of dimensionless parameters from four --
$\mathrm{Re}_E$ and the conductivity, permittivity and viscosity ratios -- to
two: a modified electric Reynolds number $\widetilde{\mathrm{Re}}$ and a
charging parameter $\varpi$. In the case $\varpi<0$, where charge relaxation in
the drop phase is slower than in the suspending phase, and, as a consequence,
the interface polarizes antiparallel to the external field, we find that above
a critical $\widetilde{\mathrm{Re}}$ value the solution exhibits a blowup
singularity such that the surface-charge density diverges antisymmetrically
with the $-1/3$ power of distance from the equator. We use local analysis to
uncover the structure of that blowup singularity, wherein surface charges are
convected by a locally induced flow towards the equator where they annihilate.
To study the blowup regime, we devise a numerical scheme encoding that local
structure where the blowup prefactor is determined by a global charging --
annihilation balance. We also employ asymptotic analysis to construct a
universal problem governing the blowup solutions in the regime
$\widetilde{\mathrm{Re}}\gg1$, far beyond the blowup threshold. In the case
$\varpi>0$, where charge relaxation is faster in the drop phase and the
interface polarizes parallel to the external field, we numerically observe and
asymptotically characterize the formation at large $\widetilde{\mathrm{Re}}$ of
stagnant, perfectly conducting surface-charge caps about the drop poles.
