Context. Generation and dissipation of magnetic fields is a fundamental physical process on the Sun. In comparison to flux emergence and the initial stages of sunspot formation, the demise of sunspots still lacks a comprehensive description. Aims. The evolution of sunspots is most commonly discussed in terms of their intensity and magnetic field. Here, we present additional information about the three-dimensional flow field in the vicinity of sunspots towards the end of their existence. Methods. We present a subset of multi-wavelengths observations obtained with the Japanese Hinode mission, the Solar Dynamics Observatory (SDO), and the Vacuum Tower Telescope (VTT) at Observatorio del Teide, Tenerife, Spain during the time period 2010 November 18−23. Horizontal proper motions were derived from G-band and Ca ii H images, whereas line-of-sight velocities were extracted from VTT echelle Hα λ656.28 nm spectra and Fe i λ630.25 nm spectral data of the Hinode/Spectro-Polarimeter, which also provided three-dimensional magnetic field information. The Helioseismic and Magnetic Imager on board SDO provided continuum images and line-of-sight magnetograms, in addition to the high-resolution observations for the entire disk passage of the active region. Results. We perform a quantitative study of photospheric and chromospheric flow fields in and around decaying sunspots. In one of the trailing sunspots of active region NOAA 11126, we observe moat flow and moving magnetic features (MMFs), even after its penumbra had decayed. We also detect a superpenumbral structure around this pore. We find that MMFs follow well-defined, radial paths from the spot all the way to the border of a supergranular cell surrounding the spot. In contrast, flux emergence near the other sunspot prevents the establishment of similar well ordered flow patterns, which could be discerned around a tiny pore of merely 2 Mm diameter. After the disappearance of the sunspots/pores, a coherent patch of abnormal granulation remained at their location, which was characterized by more uniform horizontal proper motions, low divergence values, and smaller photospheric Doppler velocities. This region, thus, differs significantly from granulation and other areas covered by G-band bright points. We conclude that this peculiar flow pattern is a signature of sunspot decay and the dispersal of magnetic flux.