How to hide homepage link from menu once logged in?
Try with this code

function THEME_menu_item_link($link) {
  global $user;
  if (empty($link['localized_options'])) {
    $link['localized_options'] = array();
  }
  if ( ($link['href'] == '&lt;front&gt;') &amp;&amp; ($user-&gt;uid == 0) ){
       return '';
  } else {
      return l($link['title'], $link['href'], $link['localized_options']);
  }
}