Transferring Mail data from one MBP to an other I try to transfer my mails, preferences and all settings from one Mac to an other. Both are using the most recent Mavericks OS X. 

I copied the ~/Library/Mail directory from the old one, as well as the ~/Library/preferences/com.apple.mail.* files. The 3 accounts seems to be working fine, and it appears, as if some of the mails have been transferred indeed, but I certainly miss the whole "ON MY MAC" folder structure form the new setup.

What is missing, where is that information stored?
In Mail.app in the "Mailboxes" section on the left side, (where Sent and Junk folders are) look toward the bottom of all the folders; there should be Smart Mailboxes and below that On My Mac folders.

It seems that some people are finding that it's hidden after they've upgraded to OS X 10.9 Mavericks. 

Next to "On My Mac" you should be a small "show/hide" as you hover over it with the mouse cursor. If you click on that hopefully you'll see those items once again.