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The giant jets represent a fundamental trace of the historical evolution ofthe outflow activity over timescales which are comparable to the accretion timeof the outflow sources in their main protostellar phase. The study of such hugejets provides the possibility of retrieving important elements related to thelife of the outflow sources. In this paper, we study the role of precession(combined with jet velocity-variability and the resulting enhanced interactionwith the surrounding environment) as a deceleration mechanism for giant jetsusing a numerical approach. We obtain predictions of H alpha intensity maps andposition-velocity diagrams from 3D simulations of the giant HH 34 jet(including an appropriate ejection velocity time-variability and a precessionof the outflow axis), and we compare them with previously publishedobservations of this object. Our simulations represent a step forward fromprevious numerical studies of HH objects, in that the use of a 7-level, binaryadaptive grid has allowed us to compute models which appropiately cover allrelevant scales of a giant jet, from the ~ 100 AU jet radius close to thesource to the ~ 1 pc length of the outflow. A good qualitative and quantitativeagreement is found between the model predictions and the observations.Moreover, we show that a critical parameter for obtaining a better or worseagreement with the observations is the ratio rho_j/rho_a between the jet andthe environmental densities. The implications of this result in the context ofthe current star formation models are discussed (ABRIDGED).Comment: 19 pages, 8 eps figs.,uses aaspp4; accepted by the Ap

The Precession of the Giant HH 34 Outflow: A Possible Jet Deceleration Mechanism