After I transfer a real estate property to another person via quit claim deed, do I own any tax on the transfer/property?

You can not transfer title in Orange County without filling a preliminary change of ownership form and indicating value for the property and paying the transfer tax as the first attorney indicated. You can only be exempt from the transfer tax if you meet one of the exceptions indicated in the form, and this will keep the value from being re-assessed for property taxes. If you do not record a Preliminary Change of ownership form with an exemption, the assessors office will re-assess the property, and one or both of you will get a transfer tax bill, and your friend will have a property tax bill in the higher assessed amount. Additionally, the transfer must be documented on YOUR tax return and YOU may owe income taxes based on the gain (if the re-assessed value is more than what you purchased it for). If you are transferring title to avoid creditors you can be sued for fraudulent transfer and the transfer can be unwound. Your friend needs to purchase it from you, pay the appropriate transfer tax, or meet an exemption, and the price can be what you paid so you will have no gain for income tax purposes.

I am not a CA attorney, laws vary from state to state, therefore you should always consult a local attorney. There is not information here to give a complete answer. CA imposes a realty transfer tax - as do certain counties and municipalities. However, there are also exemptions to the tax. So, it would depend on whether the transfer fits within one of the enumerated exemptions.