  The area entropy $A/4$ and the related Hawking temperature in the presence of
event horizons are rederived, for de Sitter and black hole topologies, as a
consequence of a tunneling of the wave functional associated to the classical
coupled matter and gravitational fields. The extension of the wave functional
outside the barrier provides a reservoir of quantum states which allows for an
additive constant to $A/4$. While, in a semi-classical analysis, this gives no
new information in the de Sitter case, it yields an infinite constant in the
black hole case. Evaporating black holes would then leave residual ``planckons"
- Planckian remnants with infinite degeneracy. Generic planckons can neither
decay into, nor be directly formed from, ordinary matter in a finite time. Such
opening at the Planck scale of an infinite Hilbert space is expected to provide
the ultraviolet cutoff required to render the theory finite in the sector of
large scale physics.
