Lots of way to do that but it really comes down to your particular circumstance. Here's the short version of our decision making on this …
1) Does the customer owe us money after we deliver? Such as getting paid by the client for each app they sell or we've set up a service / maintenance agreement with the client. If 'yes', then we'll be glad to host (for a fee, of course) the database. Why? Because then we have control. Client doesn't pay = we have leverage. Simple business.
2) If #1 above is 'no', then we want nothing to do with having to host the database. It's THEIR responsibility.