How do you REMOVE a split screen on an iMac?

You could try a an NVRAM/PRAM reset

1. Shut down your Mac.
2. Locate the following keys on the keyboard: Command (⌘), Option, P, and R. You will need to hold these keys down simultaneously in step 4.
3. Turn on the computer.
4. Press and hold the Command-Option-P-R keys before the gray screen appears.
5. Hold the keys down until the computer restarts and you hear the startup sound for the second time.
6. Release the keys.

After resetting NVRAM or PRAM, you may need to reconfigure your settings for speaker volume, screen resolution, startup disk selection, and time zone data.

If this doesn't help, you could try an SMC reset

1. Shut down the computer.
2. Unplug the computer's power cord.
3. Wait fifteen seconds.
4. Attach the computer's power cord.
5. Wait five seconds, then press the power button to turn on the computer.

Good Luck!

It looks as though a trip to an Apple store for diagnosis and possible repair is what your iMac may need.

Could be a failing or overheating GPU.

Fortunately, in the 27 inch model iMacs, the GPU is a discrete chip that can be serviced and replaced without having to replace the entire logic board.

Depending on where you live, Apple can charge anywhere from $300- $400 for replacement.

Good Luck!

See link below. There has been a recall an certain Mid 2011 27' iMac video cards

http://support.apple.com/kb/TS5167