The properties of modern TiAl-based alloys with aluminum contents around 45 at.% critically depend on the as solidified α(Ti) grain structure. Commonly, a rather coarse grain structure is obtained if α(Ti) forms via the peritectic reaction ''. Phase-field simulations have been applied to perform a case study of grain structure formation during the early peritectic growth under unidirectional growth conditions. In the absence of foreign nucleation sites, the peritectic α(Ti) phase nucleates on the dendritic surface of the properitectic β(Ti) phase. For typical values of the critical nucleation undercooling, coarse structures with large elongated grains are reproduced. A delicate interplay between nucleation and growth is predicted for reduced values of the critical undercooling. In this case, the alloy composition is found to play an additional role. An effective grain refinement by frequent nucleation is obtained, if potent nucleants can reduce the critical undercooling below the local growth undercooling. Complementary Scheil calculations and Bridgman experiments show that in situ precipitation of TiB₂ particles can be controlled by adequate boron addition. Both, numerical predictions and experiments confirm that these particles can act as effective nucleation agents and significantly reduce the grain size of α(Ti).