Hide the <none> option for required fields with default value

Make your hierarchical select field *required.

I have a "Term reference" field using "Hierarchical Select" widget and based on a two-level taxonomy tree. It's marked as "required" and has a "Default value" setted.
Even though the "<none>" option is being printed.

same here.
will look into it tomorrow.

file: hierarchical_select.module
It says in line 1670:
// Prepend a "" option to the root level when:
// - the form element is optional (1), or
// - enforce_deepest is enabled (2), or
// - the dropbox is enabled *and* at least one selection has been added to
// the dropbox (3)

So if you set "Force the user to choose a term from a deepest level", the option will show up event though the field is set to required and has a default value set.

A quick dirty fix is to edit line 1679:
$second_case = $config['enforce_deepest'];
change to:
$second_case = !$config['enforce_deepest'];

I am not sure but maybe better alternative would be:
Line 1681:
if (($first_case || $second_case || $third_case)
change to:
if (($first_case && ($second_case || $third_case))

I've solved it changing line 1684 (on 7.x-3.0-alpha5+9-dev**) from:
if (($first_case || $second_case || $third_case) && (isset($special_items) && !count($special_items['none']))) {
to
if ($first_case && ($second_case || $third_case) && (isset($special_items) && !count($special_items['none']))) {
, closed to what you said on #5-2.

**: Version 7.x-3.x-dev from 2012-Jun-16.

this no longer applies

With there being no patch I am taking the comment at #7 to indicate that the issue has been resolved in some other release.

If this is not the case please provide a patch.