  We investigate 3-dimensional almost Kenmotsu manifolds satisfying special
types of nullity conditions depending on two smooth functions $\kappa,\mu$.
When either $\kappa<-1$ and $\mu=0$ or $h=0$, such conditions coincide with the
$\kappa$-nullity condition which we show to be equivalent to the
$\eta$-Einstein one. As an application of this result, we obtain examples of
$N(\kappa)$-quasi Einstein manifolds. Moreover, for the aforementioned
manifolds, some complete local descriptions of their structure are established,
building local "models" for each of them.
