Pete on "Howe to Display defined Category (and all child cats) Assigned to a Post"

I'm using this piece of code but i'm trying to hack it so that it only displays a specified category (manually)... and all it's child categories(automatically).

<?php
$taxonomy = 'category';

// get the term IDs assigned to post.
$post_terms = wp_get_object_terms( $post->ID, $taxonomy, array( 'fields' => 'ids' ) );
// separator between links
$separator = ', ';

if ( !empty( $post_terms ) && !is_wp_error( $post_terms ) ) {

	$term_ids = implode( ',' , $post_terms );
	$terms = wp_list_categories( 'title_li=&style=none&echo=0&taxonomy=' . $taxonomy . '&include=' . $term_ids );
	$terms = rtrim( trim( str_replace( '<br />',  $separator, $terms ) ), $separator );

	// display post categories
	echo  $terms;
}

?>