eventually inhibiting freezing above a certain ‘terminal’ value of polydispersity [Sollich02]{}.

The present paper focuses on – and reviews – a number of recent attempts to investigate polydisperse phase equilibria, at least within some approximations, for another prototype model useful for studying colloidal suspensions, namely Baxter’s sticky-hard-spheres (SHS) [@Baxter68]. Here the particles are hard spheres with a surface adhesion, and the corresponding potential can be obtained as a limit of an attractive square-well which becomes infinitely deep and narrow, according to a particular prescription which ensures a finite non-zero contribution of adhesion to the second virial coefficient (‘sticky limit’). For the one-component version of this model, Baxter and collaborators [@Baxter68] solved the Ornstein-Zernike (OZ) integral equation coupled with the Percus-Yevick (PY) approximation (‘closure’). This *fully analytical* solution allows to determine all structural and thermodynamical properties of the SHS fluid. On the other hand, the multi-component PY solution, which soon followed Baxter’s work [@Perram75; @Barboy79], is practically inapplicable in the presence of significant polydispersity. In fact, it requires the computation of a set of parameters $\left\{ \Lambda
_{ij}\right\} $ determined by a system of $M(M+1)/2$ quadratic equations, which – in general – cannot be solved even numerically for a mixture with 