We investigate the dynamics of very large particles freely advected in a turbulent von Kármán flow. Contrary to other experiments for which the particle dynamics is generally studied near the geometrical center of the flow, we track the particles in the whole experiment volume. We observe a strong influence of the mean structure of the flow that generates an unexpected large-scale sampling effect for the larger particles studied. This phenomenon was not observed for neutrally buoyant particles of smaller yet finite sizes, in homogeneous and isotropic turbulence (Fiabane et al 2012 Phys. Rev. E 86 035301). We find that particles whose diameter approaches the flow integral length scale explore the von Kármán flow nonuniformly, with a higher probability to move in the vicinity of two tori situated near the poloidal neutral lines. This preferential sampling is quite robust with respect to changes of varied parameters: Reynolds number, particle density and particle surface roughness.