EN
Transport and thermodynamic properties of the well-ordered hexagonal CeAuGe compound have been studied. This compound is known to order ferromagnetically at T_{C} = 10 K with well-defined anomalies in magnetic susceptibility χ(T), electrical resistivity ρ(T) and specific heat C_p(T) characterising the phase transition. The location of T_{C} has been observed to be unstable and enhanced even in moderate applied magnetic fields. However, the dilution of magnetic species, Ce, with the non-f electron element, La, is shown in this work to achieve a continuous suppression of T_{C} to 0 K. The integrity of the space group and the details of the unit cell occupation are retained throughout the substitution series, as is the high-temperature localized Ce-effective magnetic moment μ_{eff} = 2.54 μ_{B}/(mol Ce). Our studies of physical properties down to 0.05 K show a quantum critical form of non-Fermi liquid behaviour, characterised by a logarithmic divergence in C_p(T)/T data in the very dilute Ce content.