We fabricate planar all-graphene field-effect transistors with self-aligned side-gates at 100 nm from the main graphene conductive channel, using a single lithographic step. We demonstrate side-gating below 1V with conductance modulation of 35% and transconductance up to 0.5 mS/mm at 10 mV drain bias. We measure the planar leakage along the SiO2/vacuum gate dielectric over a wide voltage range, reporting rapidly growing current above 15 V. We unveil the microscopic mechanisms driving the leakage, as Frenkel-Poole transport through SiO2 up to the activation of Fowler-Nordheim tunneling in vacuum, which becomes dominant at high voltages. We report a field-emission current density as high as 1uA/um between graphene flakes. These findings are essential for the miniaturization of atomically thin devices
