The original baitboat fishing technique using a permanent association between the fishing boat and the tuna school has been developed by the baitboat fleet of Dakar, Senegal and is also in use in the Canary Islands. This new fishing technique, the result of 20 years of improvements still on, has induced a dramatic increase of the catch yields which, in turn, has sustained the survival and even a recent development of the fleet. This technique is based on the aggregating behaviour of tropical tunas. However, it contains a dynamic component which is not found in tuna fishing on drifting or anchored fads. The specifications of the method, its refinement over the years and its main consequences for the fishery are described together with the school exchanges between baitboats over months even from one year to the next. Based on the analysis of 1228 recoveries from 5500 tagged fish, tuna movements among associated schools, between associated schools and free schools fished by purse seiners and movements in and out of the baitboat fishing grounds help to better understand the dynamics of tunas and schools of this peculiar tuna association. These data show a very high recovery rate, a remarkable tuna fidelity to the original school for all species, a small number of recoveries within the purse seine catch as well as the rare tuna movements outside the baitboat area. The study highlights the complexity and the numerous consequences of tuna and school behaviour.