Three limited samples of high-redshift radio sources of FRII-type are used to constrain the dynamical model for the jets' propagation through the two-media environment: the X-ray emitting halo with the power-law density profile surrounding the parent galaxy and the much hotter intergalactic medium (IGM) of a constant density. The model, originally developed by Gopal-Krishna and Wiita, is modified adopting modern values of its free parameters taken from recent X-ray measurements with the XMM-Newton and Chandra Observatories. We find that (i) giant-sized radio sources (≈1 Mpc) exist at redshifts up to z≈2, (ii) all newly identified the largest radio sources with 1
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