Our institution takes the application, pull credit and issue the initial disclosures. (1) We broker the loan to another institution they do underwriting who is responsible for reporting on the LAR. (2) Same circumstances except the broker bank does the underwriting.

http://www.ffiec.gov/hmda/guide.htm

Brokered or Correspondent Loans: Who Reports?
When a covered institution makes a loan through a third party such as a broker, the institution, rather than the third party, reports the loan if the institution makes the credit decision. Data on loan applications that do not result in an origination must also be reported by the entity that makes the credit decision. Consult comments 1003.1(c)-2 through -7 (Appendix D to this Guide) for more guidance.

Who reports if the borrower withdraws the application prior to the credit decision?

If the application never made it to the entity that would make the credit decision, then the bank that took the application would be responsible for reporting it as withdrawn.

That's what I thought, thanks!