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The spatial and dynamical structure of star-forming regions can help provideinsights on stellar formation patterns. The amount of data from current andupcoming surveys calls for robust and objective procedures to detect structure,so the results can be statistically analysed and different regions compared. Weprovide the community with a tool able to detect the small scale significantstructure, above random expectation, in star-forming regions, which could bethe imprint of the stellar formation process. The tool makes use of the onepoint correlation function and of nearest neighbour statistics to determine theparameters for the DBSCAN algorithm. The procedure successfully detectssignificant small scale substructures in heterogeneous regions, fulfilling thegoals it was designed for, and providing very reliable structures. The analysisof regions close to complete spatial randomness ($Q \in [0.7,0.87]$) showsthat, even when some structure is present and recovered, it is hardlydistinguishable from spurious detection in homogeneous regions due toprojection effects. Interpretation should thus be done with care. Forconcentrated regions, we detect a main structure surrounded by smaller ones,corresponding to the core plus some Poisson fluctuations around it. We arguethat these structures do not correspond to the small compact regions we arelooking for. In some realistic cases, a more complete hierarchical, multi-scaleanalysis would be needed to capture the complexity of the region. We havedeveloped implementations of our procedure, and a catalogue of the NESTs(Nested Elementary STructures) detected by it in four star-forming regions(Taurus, IC 348, Upper Scorpius, and Carina), which are publicly available tothe community. Implementations of the 3D, and up to 6D versions of theprocedure including proper movements are in progress, and will be provided asfuture work.

S2D2: Small-scale Significant substructure DBSCAN Detection I. NESTs detection in 2D star-forming regions