  The phase transition from hadronic matter to quark matter at high density
might be a strong first order phase transition in presence of a large surface
tension between the two phases. While this implies a constant-pressure mixed
phase for cold and catalyzed matter this is not the case for the hot and lepton
rich matter formed in a protoneutron star. We show that it is possible to
obtain a mixed phase with non-constant pressure by considering the global
conservation of lepton number during the stage of neutrino trapping. In turn,
it allows for the appearance of a new kind of mixed phase as long as neutrinos
are trapped and its gradual disappearance during deleptonization. This new
mixed phase, being composed by two electric neutral phases, does not develop a
Coulomb lattice and it is formed only by spherical structures, drops and
bubbles, which can have macroscopic sizes. The disappearance of the mixed phase
at the end of deleptonization might lead to a delayed collapse of the star into
a more compact configuration containing a core of pure quark phase. In this
scenario, a significant emission of neutrinos and, possibly, gravitational
waves are expected.
