The barrier to heterogeneous nucleation of the β(Ti) phase on TiB(2) and other borides has been evaluated using the plane to plane matching model. The results are compared to the known nucleation of the α(Ti) phase on the β(Ti) phase. According to this comparison, the barrier to heterogeneous nucleation of the β(Ti) phase on TiB(2) can be judged to be small. This is in agreement with inoculation experiments. The addition of a Ti-Al-TiB(2) master composite to a β(Ti) solidifying TiAl based alloy leads to a significantly refined microstructure. Microsegregations enable us to attribute this refinement to refined equiaxed β(Ti) dendrites. However, model calculations based on the hemispherical cap model predict that the refinement via heterogeneous β(Ti) nucleation should be more potent. First calculations indicate that structural imperfections of TiB(2) particles limit the nucleation site diameter. Thereby, the nucleation barrier is increased and the refinement is less pronounced.