  The formation and the evolution of protoplanetary disks are important stages
in the lifetime of stars. The processes of disk evolution and planet formation
are intrinsically linked. We spatially resolve with GRAVITY/VLTI in the K-band
the sub au-scale region of 27 stars to gain statistical understanding of their
properties. We look for correlations with stellar parameters, such as
luminosity, mass, temperature and age. Our sample also cover a range of various
properties in terms of reprocessed flux, flared or flat morphology, and gaps.
We developed semi-physical geometrical models to fit our interferometric data.
Our best models correspond to smooth and wide rings, implying that wedge-shaped
rims at the dust sublimation edge are favored, as found in the H-band. The
closure phases are generally non-null with a median value of ~10 deg,
indicating spatial asymmetries of the intensity distributions. Multi-size grain
populations could explain the closure phase ranges below 20-25 deg but other
scenarios should be invoked to explain the largest ones. Our measurements
extend the Radius-Luminosity relation to ~1e4 Lsun and confirm the significant
spread around the mean relation observed in the H-band. Gapped sources exhibit
a large N-to-K band size ratio and large values of this ratio are only observed
for the members of our sample that would be older than 1 Ma, less massive, and
with lower luminosity. In the 2 Ms mass range, we observe a correlation in the
increase of the relative age with the transition from group II to group I, and
an increase of the N-to-K size ratio. However, the size of the current sample
does not yet permit us to invoke a clear universal evolution mechanism across
the HAeBe mass range. The measured locations of the K-band emission suggest
that these disks might be structured by forming young planets, rather than by
depletion due to EUV, FUV, and X-ray photo-evaporation.
