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The static and the dynamic properties of a size-polydisperse model ionic liquid is studied using molecular dynamics simulations. Here, size of the anions is derived from a Gaussian distribution while keeping cation size fixed, resulting in a system that closely corresponds to IL mixtures with a common cation. We systematically explore the behavior of thermodynamic transition temperatures, spatial ordering of ions and the resulting screening behavior as a function of polydispersity index, $δ$. We observe a non-monotonic dependence of transition temperatures on $δ$, and this non-monotonic behaviour is also reflected in other properties such as screening length. Furthermore, from the radial distribution function analysis it is found that, upon varying $δ$, the spatial ordering of cations is affected, while no such changes is seen for anion. On the other hand, the analysis of ion motion through mean-square displacement show that for all $δ$ values considered both inertial and diffusive regimes are observed (as expected in the liquid state). However, in contrast to neutral counterpart, the overall relaxation time of the polydisperse IL system increases (and hence decreasing diffusion coefficient) with increasing $δ$.