  We use 12 cosmological $N$-body simulations of Local Group systems (the
Apostle models) to inspect the relation between the virial mass of the main
haloes ($M_{\rm vir,1}$ and $M_{\rm vir,2}$), the mass derived from the
relative motion of the halo pair ($M_{\rm tim}$), and that inferred from the
local Hubble flow ($M_{\rm lhf}$). We show that within the Spherical Collapse
Model (SCM), the correspondence between the three mass estimates is exact, i.e.
$M_{\rm lhf}=M_{\rm tim}=M_{\rm vir,1}+M_{\rm vir,2}$. However, comparison with
Apostle simulations reveals that, contrary to what the SCM states, a relatively
large fraction of the mass that perturbs the local Hubble flow and drives the
relative trajectory of the main galaxies is not contained within $R_{\rm vir}$,
and that the amount of "extra-virial" mass tends to increase in galaxies with a
slow accretion rate. In contrast, modelling the peculiar velocities around the
Local Group returns an unbiased constraint on the virial mass ratio of the main
galaxy pair. Adopting the outer halo profile found in $N$-body simulations,
which scales as $\rho\sim R^{-4}$ at $R\gtrsim R_{\rm vir}$, indicates that the
galaxy masses perturbing the local Hubble flow roughly correspond to the
asymptotically-convergent (total) masses of the individual haloes. We show that
estimates of $M_{\rm vir}$ based on the dynamics of tracers at $R\gg R_{\rm
vir}$ require a priori information on the internal matter distribution and the
growth rate of the main galaxies, both of which are typically difficult to
quantify.
