  CePd_1-xRh_x alloys exhibit a continuous evolution from ferromagnetism (T_C=
6.5 K) at x = 0 to a mixed valence (MV) state at x = 1. We have performed a
detailed investigation on the suppression of the ferromagnetic (F) phase in
this alloy using dc-(\chi_dc) and ac-susceptibility (\chi_ac), specific heat
(C_m), resistivity (\rho) and thermal expansion (\beta) techniques. Our results
show a continuous decrease of T_C (x) with negative curvature down to T_C = 3K
at x*= 0.65, where a positive curvature takes over. Beyond x*, a cusp in cac 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 -log(T/T_0) dependence of C_m/T, which transforms into a T^-q (~0.5) 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~0.75) and
increasing hybridization effects on high temperature \chi_dc and \rho.
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 > x_cr rather
the mentioned power law divergence, which coincides with a change of sign of
\beta. 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.
