  We analysed the parsec-scale linear polarization properties of 436 active
galactic nuclei (AGN) based on 15 GHz polarimetric Very Long Baseline Array
(VLBA) observations. We present polarization and total intensity images
averaged over at least five epochs since 1996 January 19 through 2019 August 4.
Stacking improves the image sensitivity down to $\sim$30 $\mu$Jy/beam and
effectively fills out the jet cross-section both in total intensity and linear
polarization. It delineates the long-term persistent magnetic field
configuration and its regularity by restoring spatial distributions of the
electric vector position angle (EVPA) and fractional polarization,
respectively. On average, about ten years of stacking period is needed to
reveal the stable and most-complete polarization distribution of a source. We
find that the degree of polarization significantly increases down and across
the jet towards its edges, typically manifesting U or W-shaped transverse
profiles, suggesting a presence of a large-scale helical magnetic field
associated with the outflow. In some AGN jets, mainly BL Lacs, we detect
quasi-constant fractional polarization profiles across the jet, accompanied by
EVPAs that closely follow the outflow. BL Lacs show higher fractional
polarization values in their cores and jets than those in quasars up to
hectoparsec de-projected scales, while on larger scales, they become
comparable. High-synchrotron-peaked BL Lac jets are found to be less polarized
than intermediate and low-synchrotron-peaked BL Lacs. The spatial distribution
of the EVPAs in BL Lacs tend to align with the local jet direction, while
quasars show an excess of orthogonal polarization orientation.
