Can I transfer application from account to account on a single tablet? I bought an android tablet to my parents for christmas. I registered it on my Google account and went on and installed some apps. (Some are the ones I own on my second tablet, some are the ones I bought specifically for them.)

Now I want to give them the tablet and register their own Google account, so they can also buy new aplications without billing my account.

Is this possible? Will all the application disappear, or can I somehow keep them on the device? (I care especially about the apps that I bought.)

(If this will turn out hard/impossible, I will just let them use my account, but well, I would rather not, since they would be able to read all my e-mail and log to my Google+ and such.)
That depends on multiple things:


if you remove your account from the device, the paid apps most likely will stop working (if they use Google License services to verify their validity). So concerning this it was a bad idea to buy those apps specifically for your parents using your account
if the device is running at least Android 4.2, you can create separate accounts for your parents, with your own account staying the "owner" (which means, you would administrate the device for them -- certain actions as e.g. factory reset are limited to the "owner account"). In this case you would need to re-install all apps with the new account -- but it would be a "fake-reinstall" (they won't be doenloaded another time). Still, above mentioned license issue will remain: Each user must pay for the app separateley.
no issue for free apps, however -- though if changing the account they might no longer update, as they are "registered" with the old account. This update issue could be fixed using the AppBrain App Market, which lets you sync the list of apps you've installed with your account (just one example, there might be other solutions I'm currently unaware of, or which might require root)


I know it's possible to have multiple accounts on a device (see e.g. Multiple Google Accounts and the Market). But never having tried this, I don't know how that works out. I think it's your parents, so you probably trust them enough to keep your account on the device, just adding a new one for them to use. This might solve the issue with the License stuff for the apps you already bought for them. But keep in mind that, depending on to which account the Playstore app defaults then, they might still ending up buying apps with your account. And, of course, they can read your mail -- not only those mails you explicitly send them, but all mail on the bound GMail account :)

However: Transfering payed apps between accounts is (currently?) not possible.

UPDATE: If your tablet is rooted, take a look at Multi-User App Share. This app permits the "owner" (first user of the device) to share apps with other accounts without having them re-download those from Google's Playstore. As for now, it is not tested thoroughly with paid apps, but should (at least partly) work. Check the app's description and comments for details.