The behaviour of the diffuse phase transition of (Pb1-xBax)(Yb1/2Nb1/2)O3 (0 less-than-or-equal-to x less-than-or-equal-to 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-epsilon 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 epsilon closely follows the Curie-Weiss law above T(N) for 0 less-than-or-equal-to x < 0. 1. Also, above x = 0.12, (1/epsilon - 1/epsilon(m)) is proportional to (T - T(t))n at T > T(t), where epsilon(m) is the peak value of epsilon at T(t) and n is an exponent. The value of n is dramatically increased for 0.1 less-than-or-equal-to x less-than-or-equal-to 0.14, and then increased linearly with increasing Ba-content (dn/dx = 1.78 x 10(-2) %-1) for 0.14 less-than-or-equal-to x less-than-or-equal-to 0.3. T(N) decreases markedly for 0 less-than-or-equal-to x < 0. 12, whereas the value of T(t) is reduced linearly with increasing x-value (dT(t)/dx = -6.61-degrees-C %-1) for 0.14 less-than-or-equal-to x less-than-or-equal-to 0.3. Another remarkable feature is an anomalous enhancement of epsilon(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 less-than-or-equal-to x < 0.1. For 0.1 less-than-or-equal-to x less-than-or-equal-to 0.14, the heat capacity anomaly is extremely broadened and a small deviation from the extrapolated baseline can be seen. In particular, we cannot detect any heat capacity anomaly associated with T(t) 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.