  The giant jets represent a fundamental trace of the historical evolution of
the outflow activity over timescales which are comparable to the accretion time
of the outflow sources in their main protostellar phase. The study of such huge
jets provides the possibility of retrieving important elements related to the
life of the outflow sources. In this paper, we study the role of precession
(combined with jet velocity-variability and the resulting enhanced interaction
with the surrounding environment) as a deceleration mechanism for giant jets
using a numerical approach. We obtain predictions of H alpha intensity maps and
position-velocity diagrams from 3D simulations of the giant HH 34 jet
(including an appropriate ejection velocity time-variability and a precession
of the outflow axis), and we compare them with previously published
observations of this object. Our simulations represent a step forward from
previous numerical studies of HH objects, in that the use of a 7-level, binary
adaptive grid has allowed us to compute models which appropiately cover all
relevant scales of a giant jet, from the ~ 100 AU jet radius close to the
source to the ~ 1 pc length of the outflow. A good qualitative and quantitative
agreement is found between the model predictions and the observations.
Moreover, we show that a critical parameter for obtaining a better or worse
agreement with the observations is the ratio rho_j/rho_a between the jet and
the environmental densities. The implications of this result in the context of
the current star formation models are discussed (ABRIDGED).
