  Aims. In this study, we analyse the magnetic field properties of a set of 15
global magnetohydrodynamics (MHD) simulations of solar-type star dynamos
conducted using the ASH code. Our objective is to enhance our understanding of
these properties by comparing theoretical results to current observations, and
to finally provide fresh insights into the field. Methods. We analysed the
rotational and magnetic properties as a function of various stellar parameters
(mass, age and rotation rate) in a 'Sun in time' approach in our extended set
of 3D MHD simulations. To facilitate direct comparisons with stellar magnetism
observations using various Zeeman-effect techniques, we decomposed the
numerical data into vectorial spherical harmonics. Results. A comparison of the
trends we find in our simulations set reveals a promising overall agreement
with the observational context of stellar magnetism, enabling us to suggest a
plausible scenario for the magneto-rotational evolution of solar-type stars. In
particular, we find that the magnetic field may reach a minimum amplitude at a
transition value of the Rossby number near unity. This may have important
consequences on the long-term evolution of solar-type stars, by impacting the
relation between stellar age, rotation and magnetism. This supports the need
for future observational campaigns, especially for stars in the high Rossby
number regime.
