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We provide a homogeneous set of structural parameters of 83 star clusters located at the periphery of the Small Magellanic Cloud (SMC) and the Large Magellanic Cloud (LMC). The clusters' stellar density and surface brightness profiles were built from deep, AO assisted optical images, and uniform analysis techniques. The structural parameters were obtained from King and Elson et al. model fittings. Integrated magnitudes and masses (for a subsample) are also provided. The sample contains mostly low surface brightness clusters with distances between 4.5 and 6.5 kpc and between 1 and 6.5 kpc from the LMC and SMC centres, respectively. We analysed their spatial distribution and structural properties, comparing them with those of inner clusters. Half-light and Jacobi radii were estimated, allowing an evaluation of the Roche volume tidal filling. We found that: (i) for our sample of LMC clusters, the tidal radii are, on average, larger than those of inner clusters from previous studies; (ii) the core radii dispersion tends to be greater for LMC clusters located towards the southwest, with position angles of $\sim$200 degrees and about $\sim$5 degrees from the LMC centre, i.e., those LMC clusters nearer to the SMC; (iii) the core radius evolution for clusters with known age is similar to that of inner clusters; (iv) SMC clusters with galactocentric distances closer than 4 kpc are overfilling; (v) the recent Clouds collision did not leave marks on the LMC clusters' structure that our analysis could reveal.