When ions or electrons are injected into an insulating liquid, they migrate towards its free surface, destabilize it, and form a charged jet. The jet then breaks into uniform drops charged at an approximately constant fraction of the Rayleigh limit, which relates the drop diameter DD to the flow rate of dielectric liquid QD and the injected current I as DD (QD/I)2/3. We have previously studied the analogous problem where the ions are substituted by nanodrops produced by a Taylor cone of a highly conducting ionic liquid (EMI-BF4) immersed in heptane or decane. This yielded hydrocarbon droplets with diameters as small as 4 μm [C. Larriba and J. Fernández de la Mora, Phys. Fluids 22, 1 (2010)], with only incidental barriers to reaching smaller sizes. Here, we overcome these barriers via silica capillaries with smaller bores. These achieve substantially smaller QD and QD/I values, resulting in drops well below the 1-2 μm measurable with a phase Doppler anemometer. Extrapolating the DD (QD/I)2/3 scaling to the smallest QD/I obtained yields calculated drop diameters of 280 nm. The current is studied as a function of QD and the ionic liquid flow rate QIL. The usual law IQIL 1/2 applies here only at small QD and high QIL. An unusual IQD -1/3 dependence appears at low QD, in contrast with the previously expected approximate independence of I on QD. This effect results from the acceleration of the dielectric jet at decreasing QD due to an increase in current given by the removal of the space charge and leading to an overall decrease in QD/I. An anomalous behavior is observed at low QD and high QIL in which the drop charge appears to exceed the Rayleigh limit. A plausible explanation is proposed based on the injection into the gas of anomalously small secondary drops and/or ions. We also investigate the injection of ionic liquid nanodrops into a quiescent liquid bath. The observed algebraic dependence of the current I V2εo/L on tip voltage V and tip to collector distance L is interpreted as resulting from two things: a current limited by space charge and an almost constant mobility Z of the nanodrops.