We study the normal-state transport properties of AFe2As2 (A = K, Rb and Cs) single crystals using Hall coefficient, resistivity and magnetoresistance (MR) measurements. In all three materials, the Hall coefficient R H shows a strong temperature dependence, which is typical for multi-band systems. In particular, R H develops an upturn below a characteristic temperature [Formula: see text], which is in agreement with the incoherence-coherence crossover reported in recent nuclear magnetic resonance studies. A Fermi-liquid-like state, characterized by T (2) behavior of the resistivity and a positive orbital MR obeying Kohler's rule, emerges below T FL ∼0.4 [Formula: see text]. The superconducting transition temperature T c experiences a simultaneous suppression with [Formula: see text] and T FL as the alkali ion's radius increases from A = K to A = Cs, suggesting that the unconventional superconductivity in the AFe2As2 series is related to the strength of the electronic coherence. A phase diagram, similar to that in the heavy fermion Kondo lattice system, is obtained. Based on all the experimental evidence, we argue that the physical properties of this family of heavily hole-doped Fe-based superconductors are controlled by the hybridization between itinerant carriers and localized orbitals, and the Kondo scenario could be effective in such a case.