We investigate the interplay between the Kondo effect and randomness in MxTiSe2 (M = Co, Ni, and Fe) single crystals. Although the typical low-T upturn of resistivity implies the Kondo effect around the single-ion Kondo temperature overline{T}_{K}, p
ositive magnetoresistance linearly proportional to the magnetic field and the power-law scaling of magnetization suggest the forbidden coexistence between Kondo effect and time reversal symmetry breaking. This puzzling result is resolved by the Griffiths scenario - disorder-induced distribution of the Kondo temperature produces an effective Kondo temperature (overline{T}_{K}) much lower than overline{T}_{K}, allowing unscreened local moments above overline{T}_{K} and resulting in non-Fermi liquid properties in MxTiSe2 below the percolation threshold (x<xc).
