  This is a sequel to the papers [OW1], [OW2]. In [OW1], the authors introduced
a canonical affine connection on $M$ associated to the contact triad
$(M,\lambda,J)$. In [OW2], they used the connection to establish a priori
$W^{k,p}$-coercive estimates for maps $w: \dot \Sigma \to M$ satisfying
$\overline{\partial}^\pi w= 0, \, d(w^*\lambda \circ j) = 0$ \emph{without
involving symplectization}. We call such a pair $(w,j)$ a contact instanton. In
this paper, we first prove a canonical neighborhood theorem of the locus $Q$
foliated by closed Reeb orbits of a Morse-Bott contact form. Then using a
general framework of the three-interval method, we establish exponential decay
estimates for contact instantons $(w,j)$ of the triad $(M,\lambda,J)$, with
$\lambda$ a Morse-Bott contact form and $J$ a CR-almost complex structure
adapted to $Q$, under the condition that the asymptotic charge of $(w,j)$ at
the associated puncture vanishes.
  We also apply the three-interval method to the symplectization case and
provide an alternative approach via tensorial calculations to exponential decay
estimates in the Morse-Bott case for the pseudoholomorphic curves on the
symplectization of contact manifolds. This was previously established by
Bourgeois [Bou] (resp. by Bao [Ba]), by using special coordinates, for the
cylindrical (resp. for the asymptotically cylindrical) ends. The exponential
decay result for the Morse-Bott case is an essential ingredient in the set-up
of the moduli space of pseudoholomorphic curves which plays a central role in
contact homology and symplectic field theory (SFT).
