  We prove several asymptotic results for partial and false theta functions
arising from Jacobi forms, as the modular variable $\tau$ tends to $0$ along
the imaginary axis, and the elliptic variable $z$ is unrestricted in the
complex plane. We observe that these functions exhibit Stokes' phenomenon - the
asymptotic behavior of these functions sharply differs depending on where the
elliptic variable $z$ is located within the complex plane. We apply our results
to study the asymptotic expansions of regularized characters and quantum
dimensions of the $(1,p)$-singlet vertex operator algebra coming from conformal
field theory. This, in particular, recovers and extends several known results
pertaining to regularized quantum dimensions, which served as a main source of
motivation.
