Aims:We describe a new form of small-scale magnetic flux emergence in the quiet Sun. This process seems to take vertical magnetic fields from subsurface layers to the photosphere, where they appear above granular convection cells. Methods: High-cadence time series of spectropolarimetric measurements obtained by Hinode in a quiet region near disk center are analyzed. We extract line parameters from the observed Stokes profiles and study their evolution with time. Results: The circular polarization maps derived from the observed Fe I 630 nm lines show clear magnetic signals emerging at the center of granular cells. We do not find any evidence for linear polarization signals associated with these events. The magnetic flux patches grow with time, occupying a significant fraction of the granular area. The signals then fade until they disappear completely. The typical lifetime of these events is of the order of 20 min. No significant changes in the chromosphere are seen to occur in response to the emergence, as revealed by co-spatial Ca II H filtergrams. The Stokes I and V profiles measured in the emerging flux concentrations show strong asymmetries and Doppler shifts. Conclusions: The origin of these events is unclear at present, but we suggest that they may represent the emergence of vertical fields lines from the bottom of the photosphere, possibly dragged by the convective upflows of granules. Preliminary inversions of the Stokes spectra indicate that this scenario is compatible with the observations, although the emergence of vertical field lines is not free from conceptual problems.