Haematopoietic stem cells (HSCs) are widely studied by HSC transplantation into immune- and blood-cell-depleted recipients. Single HSCs can rebuild the system after transplantation(1-5). Chromosomal marking', viral integration(7-9) and barcoding' of transplanted HSCs suggest that very low numbers of HSCs perpetuate a continuous stream of differentiating cells. However, the numbers of productive HSCs during normal haematopoiesis, and the flux of differentiating progeny remain unknown. Here we devise a mouse model allowing inducible genetic labelling of the most primitive Tie(2+) HSCs in bone marrow, and quantify label progression along haematopoietic development by limiting dilution analysis and data-driven modelling. During maintenance of the haematopoietic system, at least 30% or 5,000 HSCs are productive in the adult mouse after label induction. However, the time to approach equilibrium between labelled HSCs and their progeny is surprisingly long, a time scale that would exceed the mouse's life. Indeed, we find that adult haematopoiesis is largely 'sustained by previously designated 'short-term' stem cells downstream of HSCs that nearly fully self-renew, and receive rare but polydonal HSC input. By contrast, in fetal and early postnatal life, HSCs are rapidly used to establish the immune and blood system. In the adult mouse, 5-fluoruracil-induced leukopenia enhances the output of HSCs and of downstream compartments, thus accelerating haematopoietic flux. Label tracing also identifies a strong lineage bias in adult mice, with several-hundred-fold larger myeloid than lymphoid output, which is only marginally accentuated with age. Finally, we show that transplantation imposes severe constraints on HSC engraftment, consistent with the previously observed oligodonal HSC activity under these conditions. Thus, we uncover fundamental differences between the normal maintenance of the haematopoietic system, its regulation by challenge, and its re-establishment after transplantation. HSC fate mapping and its linked modelling provide a quantitative framework for studying in situ the regulation of haematopoiesis in health and disease.