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hree limited samples of high-redshift radio sources of FRII-type are used toconstrain the dynamical model for the jets' propagation through the two-mediaenvironment: the X-ray emitting halo with the power-law density profilesurrounding the parent galaxy and the much hotter intergalactic medium (IGM) ofa constant density. The model originally developed by Gopal-Krishna & Wiita(1987) is modified adopting modern values of its free parameters taken fromrecent X-ray measurements with the XMM-Newton and Chandra Observatories. Wefind that (i) giant-sized radio sources ($\sim$1 Mpc) exist at redshifts up to$z\sim 2$, (ii) all newly identified the largest radio sources with $1<z<2$appeared to be quasars, (iii) all of them are younger and expanding faster thantheir counterparts at lower redshifts, and (iv) the above properties are ratherdue to the powerful jets than peculiar environmental conditions (e.g. voids) inthe IGM. The extreme powerful jets may testify to a dominant role of theaccretion processes onto black holes in earlier cosmological epochs.

Giant Radio Sources as a probe of the cosmological evolution of the IGM,  II. The observational constraint for the model of the radio-jets propagation  through the X-ray halo--IGM interface