  The degenerate third Painleve' equation,
$u"(t)=(u'(t))^2/u(t)-u'(t)/t+1/t(-8c u^2(t)+2ab)+b^2/u(t)$, where $c=+/-1$,
$b>0$, and $a$ is a complex parameter, is studied via the Isomonodromy
Deformation Method. Asymptotics of general regular and singular solutions
$u(t)$ as $t -> +/-\infty$ and $t -> +/-i\infty$ are derived and parametrized
in terms of the monodromy data of the associated 2X2 linear auxiliary problem
introduced in the first part of this work [1]. Using these results,
three-real-parameter families of solutions that have infinite sequences of
zeroes and poles that are asymptotically located along the real and imaginary
axes are distinguished: asymptotics of these zeroes and poles are also
obtained.
