We study the hysteresis and relaxation of both intragranular and intergranular properties of TlBa 2 Ca 2 Cu 3 O y (Tl-1223) superconducting polycrystals between 80 and 120 K. The samples have been prepared using a technique involving the mixing of grains of different sizes before the final sintering. The grains show a sizeable reversible magnetization, while vortices inside the grain behave as three-dimensional objects. The transport critical current is strongly hysteretic, with features that distinguish our Tl-1223 samples from 'standard' YBa 2 Cu 3 O 7−δ (YBCO), (Hg, Re)Ba 2 Ca 2 Cu 3 O 8+δ (HBCCO) and (Bi, Pb) 2 Sr 2 Ca 2 Cu 3 O 10−δ (BSCCO) polycrystals. The preparation method improves the transport properties of the samples. The relaxation of the transport critical current density, in the presence of trapped fields, is reported here for the first time in this system, as far as we know. A phenomenological model can qualitatively describe the transport properties, where the intragrain magnetization affects the intergranular junctions, but a precise quantitative description is not achieved. The differences in the shape of the transport measurements, for different polycrystalline systems, are also well described by the model.