  We investigate outer crust compositions for a wide range of magnetic field
strengths, up to $B\simeq 4\times10^{18}$ G, employing the latest experimental
nuclear masses supplemented with various mass models. The essential effects of
the magnetic field are twoholds: 1) Enhancement of electron fraction, which is
connected to that of protons via the charge neutrality condition, due to the
Landau-Rabi quantization of electron motion perpendicular to the field, namely,
neutron-richness is suppressed for a given pressure. As a result, 2) nuclei can
exist at higher pressures without dripping out neutrons. By exploring optimal
outer-crust compositions from all possible nuclei predicted by theoretical
models, we find that neutron-rich heavy nuclei with neutron magic numbers 50,
82, 126, as well as 184, with various proton numbers emerge for $B\gtrsim
10^{17}$ G. Moreover, we show that superheavy nuclei with proton numbers
$Z\ge104$, including unknown elements such as $Z=119, 120, 122$, and/or $124$,
depending on mass models, may emerge as an equilibrium composition at bottom
layers of the outer crust for $B\gtrsim 10^{18}$ G, which are extremely
neutron-rich ($N\approx 260$-$287$, i.e., $N/Z\approx 2.2$-$2.4$). We point out
that those extremely neutron-rich superheavy nuclei locate around the next
neutron magic number $N=258$ after $N=184$, underlining importance of nuclear
structure calculations under such really exotic, extreme conditions. We
demonstrate how the superstrong magnetic field substantially alters crustal
properties of neutron stars, which may have detectable consequences.
