How to show only all the subcategories?

I’d like to show show only all the existing subcategories on a page.

I came up with this piece of code, but it unfortunately also shows the parent categories:

<?php
		if (is_category()) {
		$subcategory = get_category($cat);
		}
		if($subcategory->category_parent)
		$subcategory = wp_list_categories('orderby=title&hide_empty=0&title_li=&dept=0&exclude=1'); else
		$subcategory = wp_list_categories('orderby=title&hide_empty=0&title_li=&depth=0&exclude=1');
		if ($subcategory) { ?>

		<ul>
		<?php echo $subcategory; ?>
		</ul>

		<?php } ?>

With the list of subcategories I’d like to show automatically a word in front of each subcategory. How can I do this?

Thanks for the help!