  We use a combination of numerical and analytical methods, exploiting the
equations derived in a preceding paper, to classify all spherically symmetric
self-similar solutions which are asymptotically Friedmann at large distances
and contain a perfect fluid with equation of state $p=(\gamma -1)\mu$ with
$0<\gamma<2/3$. The expansion of the Friedmann universe is accelerated in this
case. We find a one-parameter family of self-similar solutions representing a
black hole embedded in a Friedmann background. This suggests that, in contrast
to the positive pressure case, black holes in a universe with dark energy can
grow as fast as the Hubble horizon if they are not too large. There are also
self-similar solutions which contain a central naked singularity with negative
mass and solutions which represent a Friedmann universe connected to either
another Friedmann universe or some other cosmological model. The latter are
interpreted as self-similar cosmological white hole or wormhole solutions. The
throats of these wormholes are defined as two-dimensional spheres with minimal
area on a spacelike hypersurface and they are all non-traversable because of
the absence of a past null infinity.
