It is highly desirable to undercool titanium based alloy melts and modulate their dendritic solidification process due to the relevant applications in aerospace engineering. But the serious chemical reactivities of this category of alloys result in potent heterogeneous nucleation and suppress remarkable undercoolings in the course of normal material processing. This paper shows that such a challenge can be solved by containerless processing approach. Liquid Ti-25 wt.%Al alloy is highly undercooled and rapidly solidified under containerless state by both electromagnetic levitation and drop tube techniques. Its metastable undecoolability, crystal nucleation mechanism and dendrite growth process are examined experimentally and analyzed theoretically. Those heterogeneous nuclei with wetting angles above 60 are found to be quite difficult to eliminate even during levitation processing, thus reducing the undercoolability of this alloy. The maximum undercooling of bulk alloy melt reaches 210 K (0.11 TL). The thermodynamic driving force to initiate the nucleation of -Ti phase increases almost linearly with the enhancement of undercooling. The phase dendrite displays a growth velocity up to 11.2 m/s, indicating that the rapid solidification is realized at the relatively slow cooling rate of levitated alloy melt. With the increase of undercooling, phase dendrite experiences a kinetic transition from solute diffusion controlled to thermal diffusion controlled growth. Once undercooling exceeds 100 K, the nonequilibrium solute trapping effect brings about the practically desirable segregationless solidification. Nevertheless, the single condition of substantial undercooling is insufficient to suppress the solid state transformation of phase. It is decomposed into 2-Ti3Al phase plus a small amount of -TiAl compound after containerless solidification at levitated state. A more efficient approach to controlling and modulating the solidification microstructures is to utilize the coupled effects of high undercooling and rapid quenching, which proves to be feasible through the rapid solidification of alloy droplets inside drop tube. For those alloy droplets with diameters ranging from 77 to 1048 m, their cooling rates attain a maximum of 1.05105 K/s, and the predicted maximum undercooling is 227-778 K. In this case, phase dendrites are well refined and kept in a metastable state until ambient temperature. The heat transfer calculations indicate that the thermal radiation is the dominant cooling mechanism for the large alloy droplets above 690 m, whereas thermal convection becomes the major cooling mechanism for the small alloy droplets below 690 m. The microgravity condition during free falling does not show apparent effect on the microstructural formation of these alloy droplets.