  We present first-principles relativistic particle-in-cell simulations of the
oblique pulsar magnetosphere with pair formation. The magnetosphere starts to
form with particles extracted from the surface of the neutron star. These
particles are accelerated by surface electric fields and emit photons capable
of producing electron-positron pairs. We inject secondary pairs at locations of
primary energetic particles, whose energy exceeds the threshold for pair
formation. We find solutions that are close to the ideal force-free
magnetosphere, with the Y-point and current sheet. Solutions with obliquities
$\lt 40^{\circ}$ do not show pair production in the open field line region,
because the local current density along magnetic field is below the
Goldreich-Julian value. The bulk outflow in these solutions is charge
separated, and pair formation happens in the current sheet and return current
layer only. Solutions with higher inclinations show pair production in the open
field line region, with high multiplicity of the bulk flow and the size of
pair-producing region increasing with inclination. We observe the spin-down of
the star to be comparable to MHD model predictions. The magnetic dissipation in
the current sheet ranges between 20% for the aligned rotator and 3% for the
orthogonal rotator. Our results suggest that for low obliquity neutron stars
with suppressed pair formation at the light cylinder, the presence of phenomena
related to pair activity in the bulk of the polar region, e.g., radio emission,
may crucially depend on the physics beyond our simplified model, such as the
effects of curved space-time or multipolar surface fields.
