 The exception to this is in Quarter Horse racing, where an Appendix Quarter Horse may be considered eligible to race against (standard) Quarter Horses.The designation of "Appendix" refers to the addendum section, or Appendix, of the Official Quarter Horse registry.An Appendix Quarter Horse is a horse that has either one Quarter Horse parent and one parent of any other eligible breed (such as Thoroughbred, the most common Appendix cross), two parents that are registered Appendix Quarter Horses, or one parent that is a Quarter Horse and one parent that is an Appendix Quarter Horse.