I'm looking for a way to auto-assign relationships between the current drupal user and created contact. I know there is extension CiviRelate, but it only works when using "profiles". I'm looking for a way to auto-assign selected relationships when the user creates contact from the CiviCRM backend (from the dashboard).
You could achieve this with the CiviRules extension. The extension can be found here: https://civicrm.org/extensions/civirules and the documentation here: https://docs.civicrm.org/civirules/en/latest/
You should add a rule with trigger "Contact of any type is added" and then some conditions (perhaps on contact type or contact is in group if required). You can then use the action "add relationship".