Dynamic self-organized structures with long-range order have been observed in emulsions and suspensions of particles under confined flows. Here, experiments on red blood cell suspensions under quasi-2D confined flows and numerical simulations were combined to explore long-distance self-organization as a function of the channel width, red blood cell concentration and flow rate. They reveal and quantitatively describe the existence of red blood cell long-range alignments and heterogeneous cross-stream concentration profiles characterized by red blood cell-enriched bands parallel to the flow. Numerical simulations show that, in addition to the degree of lateral confinement, the key factor for the structural self-organization of a suspension of particles under a confined flow is the deformability of the constituent particles.