  We study the deconfinement of hadronic matter into quark matter in a
protoneutron star focusing on the effects of the finite size on the formation
of just-deconfined color superconducting quark droplets embedded in the
hadronic environment. The hadronic phase is modeled by the non-linear Walecka
model at finite temperature including the baryon octet and neutrino trapping.
For quark matter we use an $SU(3)_f$ Nambu-Jona-Lasinio model including color
superconductivity. The finite size effects on the just deconfined droplets are
considered in the frame of the multiple reflection expansion. In addition, we
consider that just deconfined quark matter is transitorily out of equilibrium
respect to weak interaction, and we impose color neutrality and flavor
conservation during the transition. We calculate self-consistently the surface
tension and curvature energy density of the quark hadron inter-phase and find
that it is larger than the values typically assumed in the literature. The
transition density is calculated for drops of different sizes, and at different
temperatures and neutrino trapping conditions. Then, we show that
energy-density fluctuations are much more relevant for deconfinement than
temperature and neutrino density fluctuations. We calculate the critical size
spectrum of energy-density fluctuations that allows deconfinement as well as
the nucleation rate of each critical bubble. We find that drops with any radii
smaller than 800 fm can be formed at a huge rate when matter achieves the bulk
transition limit of 5-6 times the nuclear saturation density.
