  The exploration of the relation between galaxy sizes and other physical
parameters has provided important clues for understanding galaxy formation. We
use the CANDELS Deep+Wide surveys in the GOODS-South, UDS and EGS fields,
complemented by data from the HUDF09 program, to address the relation between
size and luminosity at z\sim7. We select 153 z-band drop-out galaxies in six
different fields characterized by a wide combination of depth and areal
coverage, ideally suited to sample without biases the observed size-magnitude
plane. Detailed simulations allow us to derive the completeness as a function
of size and magnitude and to quantify measurements errors/biases. We find that
the half light radius distribution function of z\sim7 galaxies fainter than
J=26.6 is peaked at <0.1 arcsec (or equivalently 0.5 kpc proper), while at
brighter magnitudes high-z galaxies are typically larger than ~0.15 arcsec. We
also find a well defined size-luminosity relation, Rh\simL^1/2. We compute the
Luminosity Function in the HUDF and P12HUDF fields, finding large spatial
variation on the number density of faint galaxies. Adopting the size
distribution and the size-luminosity relation found for faint galaxies at z=7,
we derive a mean slope of -1.7\pm0.1 for the luminosity function of LBGs at
this redshift. Using this LF, we find that the amount of ionizing photons
cannot keep the Universe re-ionized if the IGM is clumpy (C_HII>3) and the
Lyman continuum escape fraction of high-z LBGs is relatively low (f_esc<0.3).
With future CANDELS data, we can put severe limits to the role of galaxies in
the reionization of the Universe.
