The behaviour of the diffuse phase transition of (Pb1-xBax)(Yb12/Nb12/)O3 (0<or=x<or=0.3) ceramics has been investigated with special attention to the phase boundary near x=0.12. The temperature and frequency dependence of the dielectric constant in and loss tan delta have been carefully measured together with heat capacity measurements. Above x=0.12, the phase transition is broadened and frequency dependent, while the AFE-PE phase transition is sharp and in closely follows the Curie-Weiss law above TN for 0<or=x<0.1. Also, above x=0.12, (1/ in -1/ in m) is proportional to (T-Tt)n at T>Tt, where in m is the peak value of in at Tt and n is an exponent. The value of n is dramatically increased for 0.1<or=x<or=0.14, and then increased linearly with increasing Ba-content (dn/dx=1.78*10-2 %-1) for 0.14<or=x<or=0.3. TN decreases markedly for 0<or=x<0.12, whereas the value of Tt is reduced linearly with increasing x-value (dTt/dx=-6.61 degrees C %-1) for 0.14<or=x<or=0.3. Another remarkable feature is an anomalous enhancement of in m between x=0.1 and x=0.14. Heat capacity measurements have revealed a well-defined anomaly associated with the AFE-PE transition, increasingly broadening with Ba-content for 0<or=x<0.1. For 0.1<or=x<or=0.14, the heat capacity anomaly is extremely broadened and a small deviation from the extrapolated baseline can be seen. In particular, the authors cannot detect any heat capacity anomaly associated with Tt above x=0.14, which is suggested as additional evidence for DPT. These salient features are discussed in the light of the formation of locally ordered polar microdomains within a non-polar matrix and the pseudo-cubic structure above x=0.12.