  This work proves new probability bounds relating to the height, width, and
size of Galton-Watson trees. For example, if $T$ is any Galton-Watson tree, and
$H$, $W$, and $|T|$ are the height, width, and size of $T$, respectively, then
$H/W$ has sub-exponential tails and $H/|T|^{1/2}$ has sub-Gaussian tails.
Although our methods apply without any assumptions on the offspring
distribution, when information is provided about the distribution the method
can be adapted accordingly, and always seems to yield tight bounds.
