No. They go to the actual accounting for the property to calculate capital gains. The "$10 and other good and valuable consideration" is just legalese to satisfy the consideration requirement of the conveyance. If this is your home and you have lived in it for over 2 years, you may be exempt from paying federal captial gains tax if the capital gains is $250,000 or less.
Actively practicing law in Texas. Inactive licenses in Arizona and Georgia. All answers are general in nature and no attorney/client relationship exists in this forum.
The $10 is just part of the standard language for a quit claim deed. On a transfer of your ex's interest in the property to you in connection with your divorce, no capital gains tax should be due. When you sell the property to a third party in the future, the actual purchase price that party pays you will be the selling price used for capital gains tax purposes. If you don't already work with a good tax CPA, it may be a good idea for you to hire one to help you with these sorts of issues in the year you sell the property.
This answer is not intended to provide you with specific legal advice regarding your situation, or to create any attorney-client relationship. The intent is only to provide general information. You should be aware that you cannot rely on this answer to provide you with any protection against tax penalties. You should always consult your own attorney in order to obtain legal advice.