Q-assign also allows assigning out records using a field other than the Owner. This field can be a 'User Lookup' on that particular object. The default value of this field is 'Owner ID', which represents the normal behaviour of Q-assign i.e. to change the Owner of the object records. If you have a 'User Lookup' field on Case and you have selected this field as 'Object Owner Field', then Q-assign will assign out the records based on this field. Please note that the Owner field of the record will not change in this scenario.
Please see the screenshot below for further assistance:

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