Secular evolution of a star–planet system formed by a fast-rotating K star (M_⋆ = 0.8 M_⊙,  P_rot,ini = 1.4 days) orbited by a strongly magnetized planet (a_ini = 0.035 AU,  B_p = 10 G) in the case ofa linear B_⋆ − Ro⁻¹ relationship (in dark colors; see Eqs. (19), (20), and (21)) and a superlinear B_⋆ − Ro^−1.65 relationship (in light colors; see Eqs. (28), (29) and (30)). The thick curves correspond to our reference case discussed in Sect. 3.1.1. Top panel: semi-major axis (solid lines) and co-rotation radius of the star (black dashed lines). The gray bands on the left correspond to the disk-locking phase. Bottom panel: tidal (dark and light red) and magnetic (shades of blue) torques in the case of evolution with all the combined interactions. The red circles correspond to the crossing of the dynamical tide excitation limit by the planet.