The freshwater flux intensity is used as the main control parameter to destabilize the ThermoHaline Circulation (THC): as it increases, the classical bifurcation scenario, thermal stable steady state, millennial oscillation and haline stable steady state are reproduced in a 2D zonally-averaged ocean model under mixed boundary conditions. Both bifurcations arise through global bifurcations leading to an infinite period of the limit cycle. Here we highlight a centennial oscillation important for the instability of the thermal phase of the millennial oscillation and which could be considered as a precursor to the collapse of the THC. It is suggested that the existence or the absence of this centennial oscillation leads to dramatic changes in the collapse time scale of the THC going from several thousand years to only a few decades. This bifurcation scenario is shown to be sensitive to the value of the dissipation.