We develop an axisymmetric numerical MHD model that allows us to investigate the spatial characteristics of the interplanetary magnetic field (IMF) and key solar wind plasma parameters from 20 to 400 solar radii over all heliolatitudes. The study is aimed at an analysis of the evolution of the spatial structure of the heliosphere through the solar cycle. We consider various combinations of the relative input of the quadrupole and dipole harmonics of the solar magnetic field to imitate the solar cycle. Self-consistent solutions for the IMF, electric current, solar wind speed, density, thermal pressure, and temperature in the solar wind are obtained. The spatial evolution of the IMF and properties of quasi-stationary current sheets (QCSs) are analyzed during different phases of the solar cycle. It is shown that a classic low-latitude heliospheric current sheet is formed in the solar wind as a part of the system of longitudinal and latitudinal electric currents symmetric in the northern and southern hemispheres only during solar minimum. While the quadrupole magnetic field increases, the second QCS appears. The model successfully describes a smooth transition from the state of the fast solar wind at high heliolatitudes and the slow solar wind at low heliolatitudes at solar minimum to the solar wind speed of the same values in a wide range of heliolatitudes at solar maximum. It reproduces the actively debated phenomenon of the south–north asymmetry of the IMF in the heliosphere and shows the distribution of thermal plasma parameters consistent with observations.

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