  Based on the asymptotic analysis of ordinary differential equations, we
classify all spherically symmetric self-similar solutions to the Einstein
equations which are asymptotically Friedmann at large distances and contain a
perfect fluid with equation of state $p=(\gamma -1)\mu$ with $0<\gamma<2/3$.
This corresponds to a ``dark energy'' fluid and the Friedmann solution is
accelerated in this case due to anti-gravity. This extends the previous
analysis of spherically symmetric self-similar solutions for fluids with
positive pressure ($\gamma>1$). However, in the latter case there is an
additional parameter associated with the weak discontinuity at the sonic point
and the solutions are only asymptotically ``quasi-Friedmann'', in the sense
that they exhibit an angle deficit at large distances. In the $0<\gamma<2/3$
case, there is no sonic point and there exists a one-parameter family of
solutions which are {\it genuinely} asymptotically Friedmann at large
distances. We find eight classes of asymptotic behavior: Friedmann or
quasi-Friedmann or quasi-static or constant-velocity at large distances,
quasi-Friedmann or positive-mass singular or negative-mass singular at small
distances, and quasi-Kantowski-Sachs at intermediate distances. The
self-similar asymptotically quasi-static and quasi-Kantowski-Sachs solutions
are analytically extendible and of great cosmological interest. We also
investigate their conformal diagrams. The results of the present analysis are
utilized in an accompanying paper to obtain and physically interpret numerical
solutions.
