We investigate the conditions under which fibers can be fabricated in a microfluidic chip upon gelation of alginate with a calcium salt. We develop a device which permits us to generate a perfectly centered axial coflow and we study the influence of control parameters, namely the salt concentration, the residence time, and the size of the polymeric jet, on the gelation process. We monitor several states which include no gel, continuous fibers, pieces of gel and clogging. To describe the resulting state diagrams, we develop a model of reaction/diffusion under flow which permits us to estimate the density of links created during the gelation. While the no-gel and clogging states are chiefly governed by the density of links (respectively very low and very high), the selection of fibers against pieces-of-gel is controlled by the stress exerted on the jet at the level of the injection nozzle, also called spinneret. This simple modeling of conditions required to create fibers as an interplay between gel strength and local elongational stress might be useful for the fabrication and miniaturization of functional fibers.