Can you transfer the deed and title on a house when there is an outstanding mortgage?
In most cases, this requires the lienholder (mortgage company)'s permission. Check the closing documents carefully, but there is a generally a clause indicating that any change in title that is not approved by the lender can cause the whole loan to become due at once (called "acceleration").
Some loans are designed to be " assumable" by - that is, taken over by - others. FHA and VA loans are specifically written for this - the new owner can qualify for the loan with the lender and then take over the paymetns and transfer the deed. Still, the lender must control the process.
In the case of a divorce, death, etc the lender is generally willing to help someone assume the payments of any type of mortgage without interrupting the loan - but they still expect to be notified, and will want proof that the new borrower can afford the payments.
That said . . . . . titles transfer all the time without permission. Is this"ok?". Strictly speaking, probably not. Do the lenders actively seek retribution? Most probably don't - so long as the payments are coming in on time, they are not likely to notice and/or care. But be aware that if they DO notice or care, there could be very unintended (and often disastrous) consequences.