  Aims. The magnetic field of coronal mass ejections (CMEs) determines their
structure, evolution, and energetics, as well as their geoeffectiveness.
However, we currently lack routine diagnostics of the near-Sun CME magnetic
field, which is crucial for determining the subsequent evolution of CMEs.
Methods. We recently presented a method to infer the near-Sun magnetic field
magnitude of CMEs and then extrapolate it to 1 AU. This method uses relatively
easy to deduce observational estimates of the magnetic helicity in CME-source
regions along with geometrical CME fits enabled by coronagraph observations. We
hereby perform a parametric study of this method aiming to assess its
robustness. We use statistics of active region (AR) helicities and CME
geometrical parameters to determine a matrix of plausible near-Sun CME magnetic
field magnitudes. In addition, we extrapolate this matrix to 1 AU and determine
the anticipated range of CME magnetic fields at 1 AU representing the radial
falloff of the magnetic field in the CME out to interplanetary (IP) space by a
power law with index aB. Results. The resulting distribution of the near-Sun
(at 10 Rs ) CME magnetic fields varies in the range [0.004, 0.02] G, comparable
to, or higher than, a few existing observational inferences of the magnetic
field in the quiescent corona at the same distance. We also find that a
theoretically and observationally motivated range exists around aB = -1.6
+-0.2, thereby leading to a ballpark agreement between our estimates and
observationally inferred field magnitudes of magnetic clouds (MCs) at L1.
Conclusions. In a statistical sense, our method provides results that are
consistent with observations.
