Concerning the weblog entries search parameter, the EE docs states:
NOTE: Only custom fields of the type “Text Input”, “Textarea”, and “Drop-down Lists” are searched with this parameter.
That’s not quite true. You can use the search parameter on a relationship field to find out if a relationship has been made or not. To do it, you do not use the IS_EMPTY constant because relationship fields are never saved as empty in the database. Relationship fields without relationships are saved in the database as “0”.
So here’s is the parameter you need:
search:my_relationship_field="=0"I hope that helps someone out.