The present paper deals with the yield and transport of high-energy particle within extragalactic jet terminal shocks, also known as hotspots. We investigate in some details the cosmic ray, neutrinos and high-energy photons yield in hotspots of powerful FRII radio-galaxies by scanning all known spatial transport regimes, adiabatic and radiative losses as well as Fermi acceleration process. Since both electrons and cosmic rays are prone to the same type of acceleration, we derive analytical estimates of the maximal cosmic ray energy attainable in both toroidal and poloidal magnetic field dominated shock structures by using observational data on synchrotron emission coming from various hot-spots. One of our main conclusions is that the best hot-spot candidates for high energy astroparticle production is the extended ($L_{HS}\geq 1kpc$), strongly magnetized ($B> 0.1mG$) terminal shock displaying synchrotron emission cut-off lying at least in the optical band. We found only one object (3C273A) over the six objects in our sample being capable to produce cosmic rays up to $10^{20}$ eV. Secondly, we investigate the astroparticle spectra produced by two characteric hot-spots (Cygnus A and 3C273 A) by applying a multi-scale MHD-kinetic scheme, coupling MHD simulations to kinetic computations using stochastic differential equations. We show that 3C273 A, matching the previous properties, may produce protons up to $10^{20}$ eV in a Kolmogorov type turbulence by both computing electron and cosmic ray acceleration. We also calculate the high-energy neutrino and gamma-ray fluxes on Earth produced through p-$\gamma$ and p-p processes and compare them to the most sensitive astroparticle experiments.