Binary black hole rate density evolution normalised to the model selection results of Franciolini et al. (2021) compared to the local merger rate density inferred from GWTC-2 events assuming a power-law evolution of the merger rate with redshift. We show, in black, the contribution of all channels with relative Poisson error, in gray, computed on the detection rate of the 44 confident BBH events in the O1/O2/O3a observing runs. The model prediction can be directly compared to the local rate constrained by GWTC-2 displayed in blue. With different colors we show the contribution of each channel: common envelope (CE), stable mass transfer (SMT), globular cluster (GC) and primordial black holes (PBH). For comparison, we show the assumed SFR for isolated BBHs which the CE and SMT channels follow, in dashed gray.