Your Google account is the owner of all the files created by Form Publisher. By default, Form Publisher offers you to automatically notify people via email. It is then up to you to specify the sharing permissions and the contacts to notify.
You can share the generated files upon form submission to any contacts, and give them various permissions, similar to the sharing permissions of any Google Doc or Google Sheet: Editor / Commenter / Viewer.
You can also choose to send them a PDF, and keep that PDF in your Google Drive.
How to notify the owner ?
By default Form Publisher is configured to send a PDF at the owner when a response is submitted.
You can so choose the option "Send Link" to receive the link of document generated by Form Publisher.
How to notify people?
Two solutions are offered to you to notify your respondents. You can use them together or independently.
Method 1: Enter email addresses
On the 'Sharing options & Notifications' sidebar, click on '+ Add' and write directly the contacts' addresses in the text box:
You can then choose the permissions: Edit, comment, view, or just send them a PDF:
Method 2.a: Use the <<Username>> marker
This marker can be use if you have activated the "Collect email address" in your form settings.
Then you can put <<Username>> as a marker in the "Sharing options and notifications" sidebar and also in your template.
Method 2.b: Use a question marker
The marker can be the email address entered in one of your form fields.
For example, if you have a question titled 'Email Address', you can add the marker <<Email>> to share the document with the email address submitted by the form respondent:
Choose your sharing options (G Suite account only)
If you have asked Google Form to automatically collect the respondent's email addresses in your form settings:
Form Publisher will give you the possibility to share the document created with them, and choose the type of permissions the respondent will have: View, Edit, Comment: