That will depend on which Adobe workflow you choose to use. With PDF forms that are distributed by FormsCentral the responses are submitted to the FormsCentral servers (only the form data is submitted, not the pdf file). If you use Adobe Acrobat to distribute PDF forms, when the user clicks submit the entire PDF file can be emailed back to you or you can set it up to submit the data only to our servers.
Software Quality Engineer
Adobe Systems, Inc.