Scanning Hall probe microscopy has been used to study flux structures and dynamics in5 µm × 5 µm YBCO thin film squares, which are mesoscopic with respect to the magnetic penetration depth,λ(T), at temperaturesclose to Tc. A number of unusual vortex phenomena are observed in these microstructures which differqualitatively from the expected behaviour of more macroscopic pieces of film. Infield-cooled (FC) experiments to K a full Meissner state is generated for cooling fields less than Oe, reflecting the relatively small demagnetization factors in our samples. Cooling inhigher fields, however, results in only a very weak diamagnetic response at lowtemperatures whose magnitude is almost independent of the cooling field. In contrast weobserve considerable trapped flux upon field-removal whose magnitude grows monotonicallywith cooling field. Remarkably, all FC flux distributions exhibit almost perfect rotationalsymmetry, and can be nearly completely cancelled in a reversible fashion by tuningthe field applied to the initially FC state. Our field-cooled and zero-field-cooledresults have been analysed in terms of a Bean-like critical state model containingconstant edge and bulk current densities, and most of the observed phenomenacan be explained by considering the relative weight of these two components.Not all flux profiles can be described by our simple model, however, and undercertain circumstances symmetry-breaking ‘dipole’-like flux structures can formin several adjacent YBCO squares. We speculate that these are related to theunidirectional Ar ion milling process which was used to pattern the squares and couldhave broken the expected four-fold symmetry. We note that our results couldhave important implications for the miniaturization of thin film HTS devices.