Radial profiles for the fraction f of power dissipated in the corona (top panel) and L_2 keV (bottom panel), obtained with fixed α₀ = 0.02 and f_max = 0.5. Colors are coded according to the choice of the viscosity law: stress proportional to P_tot (P_gas + P_rad, μ = 0, black), to P_gas (μ = 1, blue), or the geometric mean of the two (μ = 0.5, red). The continuous solid, or solid-dashed, lines represent the median profiles, with the related shaded areas showing the 16th and 84th percentiles, the scatter due to the range of sources (i.e. m and ṁ) modeled. L_2 keV is proportional to the product of f and Q₊ (the accretion power per unit area). As Q₊ has very similar profiles across all models, those systems for which f is smaller produce weaker coronae in the central part. Top panel: a solid line for the median f-profile represents (thermally) stable regions of the median test source, whereas a dashed line highlights the instability regions. The vertical dot-dashed lines show instead where the median transition radius, from P_rad- to P_gas-dominated regions, lies. Refer to Sect. 2.1 for details.