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(Abridged) In this work, we study the 2.8x2.6 deg2 region in the emblematicRosette Nebula, centred at the young cluster NGC 2244, with the aim ofconstructing the most reliable candidate member list to date, determiningvarious structural and kinematic parameters, and learning about the past andthe future of the region. Starting from a catalogue containing optical tomid-infrared photometry, as well as positions and proper motions from GaiaEDR3, we apply the Probabilistic Random Forest algorithm and derive membershipprobability for each source. Based on the list of almost 3000 probable members,of which about a third are concentrated within the radius of 20' from thecentre of NGC 2244, we identify various clustered sources and stellarconcentrations, and estimate the average distance of 1489+-37 pc (entireregion), 1440+-32 pc (NGC 2244) and 1525+-36 pc (NGC 2237). The masses,extinction, and ages are derived by SED fitting, and the internal dynamic isassessed via proper motions relative to the mean proper motion of NGC 2244. NGC2244 is showing a clear expansion pattern, with an expansion velocity thatincreases with radius. Its IMF is well represented by two power laws(dN/dM\propto M^{-\alpha}), with slopes \alpha = 1.05+-0.02 for the mass range0.2 - 1.5 MSun, and \alpha = 2.3+-0.3 for the mass range 1.5 - 20 MSun, inagreement with other star forming regions. The mean age of the region is ~2Myr. We find evidence for the difference in ages between NGC 2244 and theregion associated with the molecular cloud, which appears slightly younger. Thevelocity dispersion of NGC 2244 is well above the virial velocity dispersionderived from the total mass (1000+-70 MSun) and half-mass radius (3.4+-0.2 pc).From the comparison to other clusters and to numerical simulations, we concludethat NGC 2244 may be unbound, and possibly even formed in a super-virial state.

Stellar population of the Rosette Nebula and NGC 2244: application of the probabilistic random forest