due to the lack of experimental and theoretical insights on this [@Gazzillo06]. On the other hand, few guidelines – based on arguments discussed in Refs. [@Fantoni05; @Fantoni06] – provide, as reasonable and plausible, the following dependences $$\epsilon _{ij}=\mathcal{F}(\sigma _{i},\sigma _{j})=\left\{ 
\begin{array}{ll}
\sigma _{0}^{2}/\sigma _{ij}^{2} & \mbox{Case I}~, \\ 
\sigma _{i}\sigma _{j}/\sigma _{ij}^{2} & \mbox{Case II}~, \\ 
1 & \mbox{Case IV}~, \\ 
\sigma _{0}/\sigma _{ij} & \mbox{Case V}~.%
\end{array}%
\right.   \label{eq9}$$Here $\sigma _{0}$ is a characteristic reference length (e.g. the parental mean diameter) and the numbering of the various cases follows the convention of previous work [@Fantoni05; @Fantoni06].

Figure \[fig2\] reports the results of the calculation of the cloud and shadow curves for polydisperse SHS within the simple $C_{0}$ approximation. Here and below, polydispersity is measured by an index $s$, which is the normalized standard deviation of the size distribution. Hence $s=0$ corresponds to a mono-disperse case, whereas $s=0.1$ and $s=0.3$ indicate moderate and significant polydispersity, respectively. The top panel of Fig. \[fig2\] depicts the results for case I of size-dependence of stickiness parameters. As $s$ increases, the coexistence region shrinks, thus suggesting that polydispersity *disfavours* the phase transition. On the other hand, this trend is markedly case-dependent, as illustrated in 