Drupal: How to Render Results of Form on Same Page as Form

How would I print the results of a form submission on the same page as the form itself?

Relevant hook_menu:

    $items['admin/content/ncbi_subsites/paths'] = array(
        'title' => 'Paths',
        'description' => 'Paths for a particular subsite',
        'page callback' => 'ncbi_subsites_show_path_page',
        'access arguments' => array( 'administer site configuration' ),
        'type' => MENU_LOCAL_TASK,
    );

page callback:

function ncbi_subsites_show_path_page() {
  $f = drupal_get_form('_ncbi_subsites_show_paths_form');
  return $f;
}

Form building function:

   function _ncbi_subsites_show_paths_form() {
      // bunch of code here

      $form['subsite'] = array(
        '#title' => t('Subsites'),
        '#type' => 'select',
        '#description' => 'Choose a subsite to get its paths',
        '#default_value' => 'Choose a subsite',
        '#options'=> $tmp,
      );

      $form['showthem'] = array(
        '#type' => 'submit',
        '#value' => 'Show paths',
        '#submit' => array( 'ncbi_subsites_show_paths_submit'),    
      );

      return $form;
    }

Submit function (skipped validate function for brevity)

function ncbi_subsites_show_paths_submit( &$form, &$form_state ) {
  //dpm ( $form_state );
  $subsite_name = $form_state['values']['subsite'];
  $subsite = new Subsite( $subsite_name ); //y own class that I use internally in this module
  $paths = $subsite->normalized_paths;

  // build list
  $list = theme_item_list( $paths );
}

If I print that $list variable, it is exactly what I want, but I am not sure how to get it into the page with the original form page built from 'ncbi_subsites_show_path_page'. Any help is much appreciated!

The key information in the link Nikit posted is $form_state['rebuild']. Here's some info from Drupal 7 documentation that I believe applies the same for Drupal 6...

$form_state['rebuild']: Normally, after the entire form processing is completed and submit handlers ran, a form is considered to be done and drupal_redirect_form() will redirect the user to a new page using a GET request (so a browser refresh does not re-submit the form). However, if 'rebuild' has been set to TRUE, then a new copy of the form is immediately built and sent to the browser; instead of a redirect. This is used for multi-step forms, such as wizards and confirmation forms. Also, if a form validation handler has set 'rebuild' to TRUE and a validation error occurred, then the form is rebuilt prior to being returned, enabling form elements to be altered, as appropriate to the particular validation error.