PITI payments

[Robert Carpenter]

In a PITI payment are all four portions normally paid as a lump sum to the mortgage company which then sends the accumulated insurance payments to the insurance company once a year and the accumulated tax payment in accordance with the county's billing period ? And if so what happens when the mortgage is paid off ? Shouldn't the mortgagor refund all prepaid property tax and insurance premiums to the homeowner on the day the mortgage is 'satisfied' ?