  ${T_{cc}(cc\bar{u}\bar{d})}^{+}$ has been reported by the LHCb experiment in
2022. The analysis using the Breit-Wigner parametrization found the small
binding energy, $0.273$ MeV, which is measured from the threshold of
$D^{*+}D^{0}$. In this paper, we consider $T_{cc}$ as a $DD^*$ hadronic
molecule as a deuteron-like state. The one boson exchange model is employed as
for the heavy meson interactions, where we determine the cut-off parameter
$\Lambda$ to reproduce the reported binding energy of $T_{cc}$ with
$I(J^P)=0(1^+)$. We discuss the properties of the bound state, and also search
for $T_{cc}$ with the quantum numbers other than $0(1^{+})$. Futhermore, we
analyze $T_{bb}$ as a bottom counterpart of $T_{cc}$, which involves two bottom
quarks, and obtain several bound states. Finally we consider the light-cloud
basis for wave functions of the doubly heavy tetraquarks in the heavy quark
limit. Using the basis, we find the spin multiplets of their bound states,
indicating the spin structures of diquarks in $T_{cc}$ and $T_{bb}$ with the
finite quark masses.
