Context Having recently reached the impressive milestone of 5000 confirmed extrasolar planets, the exoplanetary field has attained in less than 30 years a remarkable degree of maturity. While a purely detection-oriented phase is giving way to a subtler and more intense characterization phase, the quest for statistical trends connecting the observed properties of the exoplanet population is rapidly emerging as the next big step forward for the field. Unveiling the physical processes lurking behind the multifaceted hues of observed planetary architectures — and the limits outside which these processes no longer work — is indeed the ultimate purpose of exoplanet demographics. Still, the role played by the central star in carving these process...