  The integer quantum Hall transition (IQHT) is one of the most mysterious
members of the family of Anderson transitions. Since the 1980s, the scaling
behavior near the IQHT has been vigorously studied in experiments and numerical
simulations. Despite all efforts, it is notoriously difficult to pin down the
precise values of critical exponents, which seem to vary with model details and
thus challenge the principle of universality. Recently, M.
Zirnbauer\citep{Zirnbauer2019} [Nucl. Phys. B \textbf{941}, 458 (2019)] has
conjectured a conformal field theory for the transition, in which linear terms
in the beta-functions vanish, leading to a very slow flow in the fixed point's
vicinity which we term marginal scaling. In this work, we provide numerical
evidence for such a scenario by using extensive simulations of various network
models of the IQHT at unprecedented length scales. At criticality, we show that
the finite-size scaling of the disorder averaged longitudinal Landauer
conductance is consistent with its recently predicted fixed-point value and a
third-order expansion of RG beta functions. In the future, our numerical
findings can be checked with analytical results from the conformal field
theory. Away from criticality we describe a mechanism that could account for
the emergence of an \emph{effective} critical exponents $\nu_\mathrm{eff}$,
which is necessarily dependent on the parameters of the model. We further
support this idea by numerical determination of $\nu_\mathrm{eff}$ in suitably
chosen models.
