This is for the US from the AppleCare legal document:
Section 10: Transfer of Plan
(b)With Transfer From Original Covered Equipment to New Covered Equipment. You may make a one time, permanent transfer of the coverage under the Plan to a new Apple product that is owned and purchased by you within thirty (30) days of the Covered Equipment purchase. The new product must be eligible for coverage under the Plan and at the time of transfer both products must be covered under the manufacturer’s one (1) year limited warranty. Apple will issue a Plan Confirmation for the new product, which will then become the Covered Equipment. When notifying Apple of the transfer, you must provide the Plan Agreement Number, the serial numbers and Proof of Purchase of the products being transferred by sending or faxing, where available, notice of transfer to Apple as set forth in the section immediately above.
Note the underlined caveat.