We study the emergence of magnetic flux at very small spatial scales (less than 2") in the quiet-Sun internetwork. To this aim, a time series of spectropolarimetric maps was taken at disk center using the instrument SP/SOT on board Hinode. The LTE inversion of the full Stokes vector measured in the Fe I 6301 and 6302 Å lines allows us to retrieve the magnetic flux and topology in the region of study. In the example presented here, the magnetic flux emerges within a granular structure. The horizontal magnetic field appears prior to any significant amount of vertical field. As time goes on, the traces of the horizontal field disappear, while the vertical dipoles drift-carried by the plasma motions-toward the surrounding intergranular lanes. These events take place within typical granulation timescales.