We study both numerically and experimentally the steady cone-jet mode of electrospraying close to the stability limit of minimum flow rate. The leaky dielectric model is solved for arbitrary values of the relative permittivity and the electrohydrodynamic Reynolds number. The linear stability analysis of the base flows is conducted by calculating their global eigenmodes. The minimum flow rate is determined as that for which the growth factor of the dominant mode becomes positive. We find a good agreement between this theoretical prediction and experimental values. The analysis of the spatial structure of the dominant perturbation may suggest that instability originates in the cone-jet transition region, which shows the local character of the cone-jet mode. The electric relaxation time is considerably smaller than the residence time of a fluid particle in the cone-jet transition region (defined as the region where the surface and bulk intensities are of the same order of magnitude) except for the high-polarity case, where these characteristic times are commensurate with each other. The superficial charge is not relaxed within the cone-jet transition region except for the high-viscosity case, because significant inner electric fields arise in the cone-jet transition region. However, those electric fields are not large enough to invalidate the scaling laws that do not take them into account. Viscosity and polarization forces compete against the driving electric shear stress in the cone-jet transition region for small Reynolds numbers and large relative permittivities, respectively. Capillary forces may also play a significant role in the minimum flow rate stability limit. The experiments show the noticeable stabilizing effect of the feeding capillary for diameters even two orders of magnitude larger than that of the jet. Stable jets with electrification levels higher than the Rayleigh limit are produced. During the jet break-up, two consecutive liquid blobs may coalesce and form a bigger emitted droplet, probably due to the jet acceleration. The size of droplets exceeds Rayleigh’s prediction owing to the stabilizing effect of both the axial electric field and viscosity.