or do you take them off and the buyer gets new plates?

If you have vanity plates, you can request them back from the person who bought your car.

If you've got custom plates that you value, don't let the new owner drive away with them. The new owner has no incentive to get them back to you, and the DMV won't issue a new set if both are missing.

and you can put the originals "on hold' in your possesion for use at a later date.

the parking tickets are sent to you. Although your Bill of Sale is your proof that you aren't liable for the parking tickets, its still a hassle. When you take the plates, the new owner has immediate need to report it to the DMV and get new plates.