ditto. Once you own the plane (you or someone else built, but registered E-LSA), you visit the FSDO and can get a new certificate with your new N#/Serial# on it, which allows you to do conditional inspections. You'll need to bring your course completion certificate with you again to fsdoville. And if its E-AB (some rv-12's are registered this way), then if YOU built it then you are eligible to get a repairman certificate for it which allows you to do the "conditional/annual" inspection (and of course, anyone who can breathes air and has a pulse is allowed to work on it - E-AB or E-LSA).
Also, after some research, it would appear that if you created an LLC or corp to hold the E-LSA plane (because of a partnership, liability purposes, etc etc), then the 16-hour course doesn't do you any good because YOU do not own the plane [the LLC does]. Even if you write up an "agreement" to have your LLC lease the plane back to YOU for your own personal use, YOU don't "own" the plane. I believe in these rare cases, you'd actually need the LSRM 2 week course.