For a Cob in the EU
Where a cob is in the EU the cob's TCR registration book can accompany it's legally required EU equine identification document (ID passport).
The reason TCR can issue a registration book (a book with a breed and pedigree record) for a cob that is in the EU is because although equine identification registration (having an ID passport for an equine) is an EU legal requirement, equine studbook registration (having an ID passport with a breed and pedigree record for an equine) is not (and could not be) an EU legal requirement and it is therefore the owner's choice where (or even if) they want the breed and pedigree of their cob recorded.