Auto-filling a form field with the sender page title
You could find the referring page by using $_SERVER['HTTP_REFERER'] in PHP and then lookup the node by using drupal_lookup_path and menu_get_object. At that point you then have the node object from the previous page and you can use "$node->title" to get the title you want. 

$request_url =  $_SERVER['HTTP_REFERER'];
$host = $_SERVER['HTTP_HOST'] . "/";
$request_uri = explode($host,$request_url);
$path = drupal_lookup_path("source", $request_uri[1]);
$node = menu_get_object("node", 1, $path);


As far as how you put this into the webform, you could alter the submission using a hook or a specific component. I'm not aware of a module that lets you put PHP into a webform component. Potentially the Computed Field module (https://drupal.org/project/computed_field) could be of help. 

Help from: How to get a node by its url alias?