  Let $f$ be a transcendental entire function. It was shown in a previous paper
that the holomorphic flow $\dot z = f(z)$ always has infinitely many
trajectories tending to infinity in finite time. It will be proved here that
such trajectories are in a certain sense rare, although an example will be
given to show that there can be uncountably many. In contrast, for the
classical antiholomorphic flow $\dot z = \bar f(z)$, such trajectories need not
exist at all, although they must if $f$ belongs to the Eremenko-Lyubich class
$\mathcal{B}$. It is also shown that for transcendental entire $f$ in
$\mathcal{B}$ there exists a path tending to infinity on which $f$ and all its
derivatives tend to infinity, thus affirming a conjecture of Rubel for this
class.
