Generally, there is no recognized gain or loss on the transfer of property between spouses, or between former spouses if the transfer is because of a divorce.
A property transfer is incident to your divorce if the transfer:
Occurs within one year after the date your marriage ends, or
Is related to the ending of your marriage.
A property transfer is related to the ending of your marriage if both of the following conditions apply.
The transfer is made under your original or modified divorce or separation instrument.
The transfer occurs within 6 years after the date your marriage ends.
For tax purposes it doesn't matter how the property transfer is conducted - using quit claim or deed of gift. The deed of gift is usually used for donated properties. I would say that transferring ownership by a quit claim deed is more common.
The IRS doesn't specify when the divorce document should be created - before of after the transfer. It also allows to use your original or modified divorce or separation instrument.
However - if at the time of transfer you do not have the document - the fact that the transfer is made under your divorce or separation instrument. - may be questioned.
There are two main types of divorce instrument - divorce decree or settlement agreement.
Generally - as long as your divorce is not finalized - you are considered as married - and any property transfer between spouses is not a taxable event.
Also there no gift tax affect as long as you both are US citizens.
Yes - you may have written agreement without court approval. A transfer of property under a written agreement in settlement of marital rights or to provide a reasonable child support allowance is not subject to gift tax if you are divorced within the 3-year period beginning 1 year before and ending 2 years after the date of the agreement.