The magnetic field plays a significant role in the phenomenon of highly
collimated jets of active galactic nuclei (AGN). Relativistic effects prevent
the direct reconstruction of the magnetic field direction as transverse to
electric vectors on radio maps. We determined the topology of the
\textbf{B}-field by modeling the transverse distributions of the total and
linearly polarized intensity, polarization degree, and deviation of the
polarization direction from the local jet axis and by further comparison with
observational data. We consider (i) a helical field with a different twist
angle; (ii) a toroidal field on the jet axis surrounded by a sheath with a
longitudinal field. In the latter scenario, we consider different sheath
thickness relative to the spine. We assumed the sheath velocity is equal to or
less than that of the spine. The relativistic effects have been considered for
a general case, under which the axis and velocity vector of the jet and radial
directions do not coincide. Our simulations reproduce the main features of the
observed transverse profiles of polarization characteristics in parsec-scale
AGN jets. The model transverse distribution shapes of the polarization
properties are found to be strongly influenced by kinematic and geometric
parameters of an outflow. We demonstrated it for three AGNs having different
but typical polarization patterns revealed on radio maps. For each of these
objects, we identified the model parameters, which provide a qualitative
correspondence of theoretical profiles with those obtained from observations,
indicating that the \textbf{B}-field is strongly ordered on parsec scales.Comment: 16 pages, 11 figures, 2 table