This dataset contains all the simulations of dynamically-formed binaries performed with the software rapster, together with trained machine-learning classification models from (Antonelli, Kritos et al, in prep.), see the public codes online. All items starting with "mergers_*" are simulations of clusters and they follow the structure reported in the documentation of rapster. The simulations differ in the choice of the hyperparameters for the distribution of the cluster mass, half-mass radius and initial spin distribution for the binaries. All items starting from "RFClassifier_*" are machine-learning classification models that use a Random Forest Classifier and that are trained with the simulations above. The models ending with "*_gen" predict the generation of the black holes, those with "*_form" predict their formation channels.