  [abridged] The role of magnetic fields in the process of star formation is a
matter of continuous debate. Clear observational proof of the general influence
of magnetic fields on the early phase of cloud collapse is still pending. First
results on Bok globules with simple structures indicate dominant magnetic
fields across large spatial scales (Bertrang+2014).
  The aim of this study is to test the magnetic field influence across Bok
globules with more complex density structures. We apply near-infrared
polarimetry to trace the magnetic field structure on scales of 10^4-10^5au in
selected Bok globules. The combination of these measurements with archival data
in the optical and sub-mm wavelength range allows us to characterize the
magnetic field on scales of 10^3-10^6au.
  We present polarimetric data in the near-infrared wavelength range for the
three Bok globules CB34, CB56, and [OMK2002]18, combined with archival
polarimetric data in the optical wavelength range for CB34 and CB56, and in the
sub-millimeter wavelength range for CB34 and [OMK2002]18. We find a strong
polarization signal (P>2%) in the near-infrared and strongly aligned
polarization segments on large scales (10^4-10^6au) for all three globules.
  This indicates dominant magnetic fields across Bok globules with complex
density structures.
  To reconcile our findings in globules, the lowest mass clouds known, and the
results on intermediate (e.g., Taurus) and more massive (e.g., Orion) clouds,
we postulate a mass dependent role of magnetic fields, whereby magnetic fields
appear to be dominant on low and high mass but rather sub-dominant on
intermediate mass clouds.
