  We report the relativistic coupled cluster study of the hyperfine structure
and effect of the nuclear magnetization distribution (Bohr-Weisskopf effect) in
the $6P_{1/2}$, $6P_{3/2}$ and $7S_{1/2}$ states of several Tl isotopes. It is
shown that the Gaussian basis set can be used in such electronic structure
calculations and provide a good accuracy. For the ground electronic state of
the neutral Tl atom achieved uncertainty for the hyperfine structure constant
is smaller than 1\%. A strong Bohr-Weisskopf correction (about 16\%) was found
for the $6P_{3/2}$ state which can be of interest for the nuclear structure
theory. Basing on the theoretical treatment as well as the available
experimental data nuclear magnetic moments of short lived ${}^{191}$Tl and
${}^{193}$Tl isotopes were also predicted.
