The CePd 1−x Rh x alloy exhibits a continuous evolution from ferromagnetism ͑T C = 6.5 K͒ at x = 0 to a mixedvalence ͑MV͒ state at x = 1. We have performed a detailed investigation on the suppression of the ferromagnetic ͑F͒ phase in this alloy using dc ͑ dc ͒ and ac ͑ ac ͒ susceptibility, specific heat ͑C m ͒, resistivity ͑͒, and thermal expansion ͑͒ techniques. Our results show a continuous decrease of T C ͑x͒ with negative curvature down to T C =3 K at x * = 0.65, where a positive curvature takes over. Beyond x * , a cusp in ac is traced down to T C * =25 mK at x = 0.87, locating the critical concentration between x = 0.87 and 0.90. The quantum criticality of this region is recognized by the −log͑T / T 0 ͒ dependence of C m / T, which transforms into a T −q ͑q Ϸ 0.5͒ one at x = 0.87. At high temperature, this system shows the onset of valence instability revealed by a deviation from Vegard's law ͑at x V Ϸ 0.75͒ and increasing hybridization effects on high-temperature dc and ͑T͒. Coincidentally, a Fermi liquid contribution to the specific heat ͑␥͒ arises from the MV component, which becomes dominant at the CeRh limit. In contrast to antiferromagnetic systems, no C m / T flattening is observed for x Ͼ x cr but, rather, the mentioned power-law divergence, which coincides with a change of sign of ͑T͒. The coexistence of F and MV components and the sudden changes in the T dependencies are discussed in the context of randomly distributed magnetic and Kondo couplings.