  In the present work, the $^{204-210}$Tl isotopes have been investigated by
performing large-scale shell-model calculations, including configurations
allowing both neutron and proton core excitations across the $Z$ = 82 and $N$ =
126 shell gaps. Inspired by the recent high-spin experimental data, the
structure of Tl isotopes has been studied for a considerably large model space.
The KHHE interaction has been used for $^{204-206}$Tl isotopes, KHH7B
interaction for $^{204-210}$Tl isotopes, and additionally KHM3Y interaction has
been used for $^{208}$Tl isotope. The core excitation has been performed using
the KHH7B and KHM3Y interactions. The level spectra of $^{204-210}$Tl isotopes
are comprehensively described and explained by multi-nucleon couplings of
single-particle-hole orbitals within the valence space and by core excitations
across $^{208}$Pb core. The well-known isomeric states are analyzed in terms of
the shell model configurations.
