Laser-ablated Tl atoms react with dihydrogen in excess neon, pure hydrogen, and excess argon to form primarily the TlH diatomic molecule. Ultraviolet irradiation increases weak bands that are identified as TlH2 and TlH3 on the basis of D-2 and HD substitution and density functional theory (DFT) isotopic frequency calculations. Sample annealing fosters the dimerization of TlH to give Tl2H2 with a rhombic ring structure and the TlTlH2 isomer. The markedly lower yield of TlH3 in these experiments compared to AlH3 in earlier investigations is due to the expected decrease in stability for the Tl(III) oxidation state. The Tl+(H-2)(n) cation complex is also observed, and trends within the group 13 metals are summarized. Excitation at 193 nm gives the S-2(1/2) --> P-2(1/2.3/2) doublet for unreacted Tl atoms, which is blue-shifted 660 cm(-1) from the gas-phase value in solid D-2 but only 210 cm(-1) in solid H-2, owing to the smaller, more repulsive D-2 matrix cage.