  Relativistic discrete ejecta launched by black hole X-ray binaries (BH XRBs)
can be observed to propagate up to parsec-scales from the central object.
Observing the final deceleration phase of these jets is crucial to estimate
their physical parameters and to reconstruct their full trajectory, with
implications for the jet powering mechanism, composition and formation. In this
paper we present the results of the modelling of the motion of the ejecta from
three BH XRBs: MAXI J1820+070, MAXI J1535$-$571 and XTE J1752$-$223, for which
high-resolution radio and X-ray observations of jets propagating up to $\sim$15
arcsec ($\sim$0.6 pc at 3 kpc) from the core have been published in the recent
years. For each jet, we modeled its entire motion with a dynamical blast-wave
model, inferring robust values for the jet Lorentz factor, inclination angle
and ejection time. Under several assumptions associated to the ejection
duration, the jet opening angle and the available accretion power, we are able
to derive stringent constraints on the maximum jet kinetic energy for each
source (between $10^{43}$ and $10^{44}$ erg, including also H1743$-$322), as
well as placing interesting upper limits on the density of the ISM through
which the jets are propagating (from $n_{\rm ISM} \lesssim 0.4$ cm$^{-3}$ down
to $n_{\rm ISM} \lesssim 10^{-4}$ cm$^{-3}$). Overall, our results highlight
the potential of applying models derived from gamma-ray bursts to the physics
of jets from BH XRBs and support the emerging picture of these sources as
preferentially embedded in low-density environments.
