  The propagation of extragalactic jets is studied by a series of twelve
axisymmetric hydrodynamic simulations. Motivated by observational constraints,
but unlike most previous simulations, the regime of jet to external medium
density (eta) from 10^-5 to 10^-2 is explored, for Mach numbers (M) between 2.6
and 26. The computational domain contained the bow shocks for the whole
simulation time. The bow shocks are found to be spherical at source sizes below
a critical value r1 (blastwave phase), which can reach up to 10 jet radii.
[...] The numerical work is complemented by an analytic approach for the
spherical phase. Extending previous work, the radial force balance could be
integrated for arbitrary background density and energy input, which results in
a global solution. The analytic results are shown to be consistent with the
numerical work, and a lower limit to r1 can be calculated, which falls below
the numerical results by a few jet radii. It is shown explicitely how a King
density distribution changes the discussed aspects of the bow shock
propagation. Because the jet head propagates very fast in the blastwave phase,
it turns out that it is not possible to ``frustrate'' a jet by a high density
environment. This is very important for the class of small radio galaxies
(compact symmetric objects / GHz peaked sources): They have to be young. During
its blastwave phase, a powerful jet can transfer typically 10^60 erg to the
environmental gas. This is enough to balance the radiative losses in a cooling
flow, if one of the cluster galaxies harbours a powerful jet every Gigayear.
