High-quality KFe2As2 single crystals have been studied by transport, magnetization and low-T specific heat measurements. Their analysis shows that superconductivity occurs (in some cases coexists) in the vicinity of disordered magnetic phases (Griffiths and spin-glass type) depending of the amount of local magnetic moments (probably excess Fe derived)and sample inhomogeneity. The achieved phenomenological description of our data including also data from the literature provides a consistent explanation of the observed non-Fermi-liquid behavior and of the nominally large experimental Sommerfeld coefficient gamma_n about 94 mJ/mol K^2. We suggest that the intrinsic value (directly related to the itinerant quasi-particles) gamma_el about 60(10)mJ/mol K^2 is significantly reduced compared with gamma_n. Then an enhanced relative jump of the electronic specific heat Delta C_el/gamma_el T_c about 0.8 and a weak total electron-boson coupling constant lambda less or about 1 follow.
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