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The group of dimensionless physical parameters is considered in attempts to constrain and evaluate the role of magnetic fields by scaling laws and orders of magnitudes. Admissible combinations are numerous and include the binary interplay of independent parameter combinations of magnetic fields with local and global plasma density, velocity, temperature, composition, ionization degree, radiation and other quantities including kinetic distribution function details in different space-time scales. It makes the overall situation very diversified and not obeying any a priori general scenario and model. The role of magnetic fields in the visible Universe is varying from primary to negligible for many known astrophysical objects and phenomena. The question about the bulk role of magnetic fields in the Universe is ill posed and has no definite answer because of not known boundary conditions in space and time. Available observations are not sufficient to quantify magnetic fields in several instances and for the whole visible Universe in the same manner as the ‘critical density of matter’ in the homogeneous model. http://www.exul.ru/img/Workshop-program_final.pdf