  An inflating brane-world can be created from ``nothing'' together with its
Anti-de Sitter (AdS) bulk. The resulting space-time has compact spatial
sections bounded by the brane. During inflation, the continuum of KK modes is
separated from the massless zero mode by the gap $m=(3/2) H$, where $H$ is the
Hubble rate. We consider the analog of the Nariai solution and argue that it
describes pair production of ``Black cigars'' attached to the inflating brane.
In the case when the size of the instantons is much larger than the AdS radius,
the 5-dimensional action agrees with the 4-dimensional one. Hence, the 5D and
4D gravitational entropies are the same in this limit. We also consider thermal
instantons with an AdS black hole in the bulk. These may be interpreted as
describing the creation of a hot universe from nothing, or the production of
AdS black holes in the vicinity of a pre-existing inflating brane-world. The
Lorentzian evolution of the brane-world after creation is briefly discussed. An
additional "integration constant" in the Friedmann equation -accompanying a
term which dilutes like radiation- describes the tidal force in the fifth
direction and arises from the mass of a spherical object inside the bulk. This
could be a 5-dimensional black hole or a "parallel" brane-world of negative
tension concentrical with our brane-world. In the case of thermal solutions,
and in the spirit of the $AdS/CFT$ correspondence, one may attribute the
additional term to thermal radiation in the boundary theory. Then, for
temperatures well below the AdS scale, the entropy of this radiation agrees
with the entropy of the black hole in the AdS bulk.
