what would be the (tax taxable) value of a property, released through a quit claim deed, for tax purposes for the grantee when grantee sells the it

If you are asking about the tax assessed value for real property taxes, that is based upon the fair market value of the property.  You should ask the local county's property appraiser's office for the calculation. If you are asking about the amount upon which documentary stamp tax would be based for the transfer, the Florida Department of Revenue would seek tax based upon the consideration being exchanged. If this is unencumbered property for no consideration, then only nominal (i.e., 70 cents) documentary stamp tax would be due. The foregoing is specific to the law and procedure in Florida.  This response does not constitute legal advice as the facts presented are limited and unstated facts will likely impact your particular situation. This response is intended for general education only and does not create an attorney-client relationship. Please schedule a consultation with a local attorney for more specific and detailed answers to your legal issues.