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We derived surface brightness profiles in the \emph{g} band for 170 SmallMagellanic Cloud (SMC) star clusters (SCs) mainly located in the central regionof the galaxy. We provide a set of homogeneous structural parameters obtainedby fitting Elson, Fall \& Freeman (EFF) and King models. Through a carefulanalysis of their colour-magnitude diagrams (CMDs) we also supply the ages fora subsample of 134 SCs. For the first time, such a large sample of SCs in theSMC is homogeneously characterized in terms of their sizes, luminosities andmasses, widening the probed region of the parameter space, down to hundreds ofsolar masses. We used these data to explore the evolution of the SC'sstructural parameters with time. In particular, we confirm the existence of aphysical mechanism that induces an increase of the core radius after 0.3-1.0Gyr. We suggest that cluster mass could be the main parameter driving the innerexpansion, as none of the SCs having $\log (M/M_{\odot}) \leq 3.5$~dex analysedin this work undergoes to such an expansion. We also detected a mass-sizerelationship almost over the entire range of SCs masses investigated here.Finally, our data suggest that globally the SMC SC system is dynamicallyevolved.

STEP Survey II: Structural Analysis of 170 star clusters in the SMC