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The latest results of the most detailed analysis of multi-epoch polarization-sensitive observations of active galactic nuclei (AGN) jets at parsecs scales by very long baseline interferometry (VLBI) reveal several characteristic patterns of linear polarization distribution and its variability [1, 2]. Some of the observed profiles can be reproduced by a simple model of a jet threaded by a helical magnetic field. However, none of the models presented to date can explain the observed polarization profiles with an increase in its degree towards the edges of the jet, and accompanied by a "fountain" type electrical vector pattern and its high temporal variability in the center. Based on simulations of the VLBI observations of relativistic jets, we show here that the observed transverse linear polarization profiles can be naturally produced in a model of jets precessing on ten-years scales. In this scenario, due to the finite resolution of VLBI arrays, the initially strong polarization along the jet axis is blurred due to the superposition of regions whose polarization angle changes significantly when projected onto the sky plane. In our simulations, we qualitatively reproduce the distribution of the electric vector and its variability, though the polarization distribution images are characterized by a bright spine due to weak suppression of polarized emission, which is poorly consistent with observations of quasars. More effective depolarization can be obtained in models with the suppressed emission of the jet spine. [ABSTRACT FROM AUTHOR]