  Suppose that $\Sigma$ is a closed and oriented surface equipped with a
Riemannian metric. In the literature, there are three seemingly distinct
constructions of open books on the unit (co)tangent bundle of $\Sigma$, having
complex, contact, and dynamical flavors, respectively. Each one of these
constructions is based on either an admissible divide or an ordered Morse
function on $\Sigma$. We show that the resulting open books are pairwise
isotopic provided that the ordered Morse function is adapted to the admissible
divide on $\Sigma$. Moreover, we observe that if $\Sigma$ has positive genus,
then none of these open books are planar and furthermore, we determine the only
cases when they have genus one pages.
