Listing children in parent taxonomy

This function? taxonomy_get_children

While you are there spend some time in the API it is worth getting to know.

Use an URL like /taxonomy/term/35/all

"all" is the depth. It could be a number.

There is a module which makes "all" the default behavior (http://drupal.org/project/taxonomy_forceall) but it doesn't have an Drupal 6 version.

Or, use the views module to generate your custom taxonomy lists.