  Quantum creation of Universes with compact spacelike sections that have
curvature $k$ either closed, flat or open, i.e. $k=\pm1,0$ are studied. In the
flat and open cases, the superpotential of the Wheeler De Witt equation is
significantly modified, and as a result the qualitative behaviour of a typical
wavefunction differs from the traditional closed case. Using regularity
arguments, it is shown that the only consistent state for the wavefunction is
the Tunneling one. By computing the quantum probabilities for the curvature of
the sections, it is shown that quantum cosmology actually favours that the
Universe be open, $k=-1$. In all cases sufficient inflation $\sim 60$
e-foldings is predicted: this is an improvement over classical measures that
generally are ambiguous as to whether inflation is certain to occur.
