VLBI polarization data show magnetic field configuration parallel to the nuclear jet in quasars and perpendicular to it in BL Lac objects. It appears difficult to account for this contrast within the unified scheme for AGN. To investigate a direct explanation of this peculiarity of BL Lac objects, we study the possibilities of propagation and radiation of beams of particles in transverse ambient magnetic field. High energy streams with kinetic energy density larger than the ambient magnetic one, Ekin > Emag, can easily propagate with enhancement of the transverse magnetic field at the leading edge of the stream and reconnection of magnetic lines in its wake. Synchrotron radiation in front shocks naturally leads to the observed polarization. Moreover self-polarization, with formation of charge layers and E × B drift velocity, allows substantial propagation for even lower energy streams with Ekin < Emag, as long as their density no is large enough, typically κ = 4πnomic2/B2 > 1. Such low energy streams are non diamagnetic and do not modify the ambient field. Any high energy tail of the total particle distribution in the jet therefore radiates in the transverse field pattern. This concerns for instance the BL Lac object W Comae if we assume a proton-electron jet with bulk velocity vo = 0.1c (as the source does not require relativistic beaming so far), an equipartition magnetic field B = 0.02 G and a density of radiating particles nr = 0.05cm−3 at about 7 pc from the nucleus (knot K3). For nr/no = 10−3, one gets the stream density no = 50cm−3 which allows good propagation as κ reaches 2 × 103, and still corresponds to a moderate mass outflow of 0.06 M⊙ /year for a VLBI jet cross-sectional area of 2pc2.