We examine the form of clusters and islands formed by oxides and halides on ionic substrates where there is an appreciable lattice mismatch between substrate and adsorbate. Structures are optimised in the static limit using both periodic density functional theory and atomistic simulation techniques. Results are presented for three examples: (i) CaO on the (100) surface of BaO, (ii) CaF2 on the (110) and (111) surfaces of BaF2,(iii) Bi2O3 on the SrO-terminated (100) surface of SrTiO3. In none of these do we observe direct overlay of groups of ions over substrate ions, accompanied by marked changes in bond lengths in the adsorbate cluster or layer. Rather, islands have a critical maximum domain size because larger islands would result in unfavourable electrostatic interactions between adsorbate and substrate. Instead loops or gaps or other defect regions form between individual islands. For Bi2O3 we propose the low temperature stabilization of the superionic delta-phase of Bi2O3 on deposition on (100) SrTiO3 is not a consequence of epitaxial matching of Bi center dot center dot center dot Bi with Sr center dot center dot center dot Sr, as previously suggested, but rather due to the mismatch between the Bi-O and Sr-O bond lengths. This gives rise to individual Bi-O islands, which promote the formation of a disordered surface phase. We find no evidence for the stabilization of a symmetric cubic structure. The formation of the disordered Bi2O3 ultrathin film is also associated with a decrease in the band gap.