Context. In high-mass (=7 M?) star formation (SF) studies, high-angular resolution is crucial for resolving individual protostellar outflows (and possibly accretion disks) from the complex contribution of nearby (high- and low-mass) young stellar objects (YSO). Previous interferometric studies have focused mainly on single objects. Aims: A sensitive survey at high angular resolution is required to investigate outflow processes in a statistically significant sample of high-mass YSOs and on spatial scales relevant to testing theories. Methods: We selected a sample of 40 high-mass YSOs from water masers observed within the BeSSeL Survey. We investigated the 3D velocity and spatial structures of the molecular component of massive outflows at milli-arcsecond angular resolution using multi-epoch Very Long Baseline Array (VLBA) observations of 22 GHz water masers. We also characterize the ionized component of the flows using deep images of the radio continuum emission with resolutions of ~0."2, at 6, 13, and 22 GHz with the Jansky Very Large Array (JVLA). Results: We report the first results obtained for a subset of 11 objects from the sample. The water maser measurements provide us with a very accurate description of the molecular gas kinematics. This in turn enables us to estimate the momentum rate of individual outflows, varying in the range 10-3-100M? yr-1 km s-1, among the highest values reported in the literature. In all the observed objects, the continuum emission at 13 and 22 GHz has a compact structure, with its position coincident with that of the water masers. The 6 GHz continuum consists of either compact components (mostly well aligned with the 13 and/or 22 GHz sources) or extended emission (either highly elongated or approximately spherical), which can be offset by up to a few arcseconds from the water masers. The unresolved continuum emission associated with the water masers likely points to the YSO location. The comparison of the radio continuum morphology to the maser spatial and 3D velocity distribution shows that five out of elevenhigh-mass YSOs emit a collimated outflow, with a flow semi-opening angle in the range 10°-30°. The remaining six sources present a more complicated relationship between the geometry of the radio continuum and water maser velocity pattern; therefore, no firm conclusions can be drawn regarding their outflow structure. In two sources, the 6 GHz continuum emission shows a highly elongated structure with a negative spectral index down to -1.2. We interpret this finding in terms of synchrotron emission from relativistic electrons accelerated in strong shocks, which indicates that non-thermal continuum emission could be common in high-mass protostellar jets. The Lyman continua derived from bolometric luminosities always exceed those obtained from the radio luminosities. Conclusions: These first results suggest that collimated outflows or jets can be common in high-mass YSOs and, in a couple of cases, provide hints that magnetic fields could be important in driving these jets. To draw firmer conclusions, however, we await completion of the analysis for the entire sample of 40 high-mass YSOs.
