3 loops, no duplicates

First loop (I show the last 3 sticky posts)

<?php $do_not_duplicate = array();
  $my_query = new WP_Query(array('posts_per_page' => 3, 'post__in' => get_option( 'sticky_posts' ), 'caller_get_posts' => 1 ) );
  while ($my_query->have_posts()) : $my_query->the_post();
  $do_not_duplicate[] = $post->ID; ?>

  HTML CODE HERE

<?php endwhile;?>
<?php wp_reset_query(); ?>

Second loop (the 4 latest posts, excluding stickies)

<?php ////$do_not_duplicate = array();////remove this; this line is only allowed once before the first loop
  $my_query = new WP_Query(array('posts_per_page' => 4, 'post__not_in' => array_merge($do_not_duplicate, get_option( 'sticky_posts' ) ) ) );
  while ($my_query->have_posts()) : $my_query->the_post();
  $do_not_duplicate[] = $post->ID; ?>

    HTML CODE HERE

<?php endwhile;?>
<?php wp_reset_query(); ?>

Third loop (showing the latest post from each cateogry, excluding stickies)

<?php
$cat_args=array(
  'orderby' => 'name',
  'order' => 'ASC'
   );

////$do_not_duplicate = array();////remove this; this line is only allowed once before the first loop

$categories=get_categories($cat_args);
  foreach($categories as $category) {
    $args=array(
      'posts_per_page' => 1,
      'post__not_in' => array_merge($do_not_duplicate,get_option( 'sticky_posts' )),
      'category__in' => array($category->term_id),
    );
    $posts=get_posts($args);
      if ($posts) {
        $ncat = '<a href="' . get_category_link( $category->term_id ) . '" title="' . sprintf( __( "View all posts in %s" ), $category->name ) . '" ' . '>' . $category->name.'</a>';
        foreach($posts as $post) {
          setup_postdata($post);
		  $do_not_duplicate[] = $post->ID; ?>

	HTML CODE HERE

          <?php
        }
      }
    }
?>

<?php wp_reset_query(); ?>