Hi Fruit tingles,
I had an unplanned free birth- there's a link in my siggy if you want to read my birth story. I did call an ambulance and was transferred to the hospital, but released about 5 hours later at my own request. I had no problems with paperwork but I did get a call from Births Deaths and Marriages, who in turn contacted my midwife (a public mw, but through a caseload program, so different to your situation) to confirm the baby was a live birth. I was admitted straight to the maternity ward, bypassing emergency (although the ambos did warn i may go there, depending on hospital protocol). I had the choice of whether we wanted the cord cut or not by the ambos, but they discouraged me from delivering the placenta until we reached the hospital.

I hope that's useful info for you There is a lot of good info on 'emergency birthing' if you have a Google