The initial warranty is based on the serial number. When you need service or support that's the first thing they ask for. If you do want apple care, then you should buy it yourself, in your name, because transferring apple care is much more complicated.
You can read the entire thing
here.
6. Transfer of Plan
You may transfer this Plan to a new owner of the Covered Equipment by sending or faxing notice of transfer to AppleCare Administration, P.O. Box 149125, Austin, TX 78714 — 9125, U.S. (fax number 512 — 674 — 8125). You must provide the Plan Agreement Number, the serial numbers of the Covered Equipment being transferred, proof of purchase of the Plan, and the name, address, telephone number and email address of the new owner.
edit-added the transfer info
Message was edited by: 1.21 Gigaflops