The liquid cone-jet mode can be produced upon stimulation by a coflowing gas sheath. Most applications deal with the jet breakup, leading to either of two droplet generation regimes: Jetting and dripping. The cone-jet flow pattern is explored by direct axisymmetric volume of fluid (VOF) numerical simulation; its evolution is studied as the liquid flow rate is increased around the jetting-dripping transition. As observed in other focused flows such as electrospraying cones upon steady thread emission, the flow displays a strong recirculating pattern within the conical meniscus; it is shown to play a role on the stability of the system, being a precursor to the onset of dripping. Close to the minimum liquid flow rate for steady jetting, the recirculation cell penetrates into the feed tube. Both the jet diameter and the size of the cell are accurately estimated by a simple theoretical model. In addition, the transition from jetting to dripping is numerically analyzed in detail in some illustrative cases, and compared, to good agreement, with a set of experiments.