  We investigate the nature of trions, pairing and quantum phase transitions in
one-dimensional strongly attractive three-component ultracold fermions in
external fields. Exact results for the groundstate energy, critical fields,
magnetization and phase diagrams are obtained analytically from the Bethe
ansatz solutions. Driven by Zeeman splitting, the system shows exotic phases of
trions, bound pairs, a normal Fermi liquid and four mixtures of these states.
Particularly, a smooth phase transition from a trionic phase into a pairing
phase occurs as the highest hyperfine level separates from the two lower energy
levels. In contrast, there is a smooth phase transition from the trionic phase
into a normal Fermi liquid as the lowest level separates from the two higher
levels.
