Get the children categories of a category

getChildrenCategories.php

<?php $catname =single_cat_title("",false);
$catId= get_cat_ID($catname);?>
<ul>
<?php
wp_list_categories("orderby=id&show_count=0&use_desc_for_title=1&child_of=$catId");
?>
</ul>

Use single_cat_title() instead wp_title(). The first is more secure than wp_title(). The whole of SEO plugins can change the title, and use the wp_title() method to do this. If title!=category name don't causes an error, but you can see all of the categories of your blog.