Custom Post Conditional for Parent & Child Single.php?

I guess that you should change the order to first check if there is any parent:

<?php if ( is_home() || is_page( 'overview' ) || is_page( 'about' )  ) : ?>
    Home Page
<?php elseif ( $post->post_parent > 0 ): ?> 
 artist   child
<?php elseif ( 'artists' == get_post_type() ): ?>
    artist parent               
<?php else : ?>
 empty other pages etc

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