I had purchased the newest Samsung branded MHL Adapter (ET-H10FAUWESTA) to play games full screen on my Samsung TV. The Samsung TV even has an HDMI port that is labelled MHL. That adapter is white and it clearly has the 11-pin connector.
Technically this adapter "works" in that it a 1080p30 (1080p at 30Hz) image appears on the TV. However, this adapter explicitly advertises 1080p60 when used with the Samsung Galaxy S4. Sadly, the 60Hz feature is an epic fail.
In the manual it comes with it advertises that CEC can be used to send remote control key presses to the phone so you can navigate the phone with the TV remote (or as Samsung calls it: Anynet+). This feature also does not work. The Samsung TV does not detect any CEC device attached. When I try pressing buttons on the TV, the TV just says "Function not supported".
But before you go ahead and assume that 1080p30 will be sufficient, note that when you play games on the TV with this adapter, the framerate will be 30Hz and not 60Hz. This will cause most games to run at 1/2 speed (like all the Sonic the Hedgehog games).
Also note that the 11-pin connector on this adapter only "wires" the 6 MHL pins out. The 5 USB pins are left unconnected. To get the phone to charge while this adapter is attached, you must connect the USB charger to it.
Pretty much everything advertised about this adapter is wrong (except for 1080p30).
I should also note that I have the Verizon SCH-I545 Galaxy S4. This may be a Verizon only problem because I have seen the YouTube video where a guy in the UK explicitly demonstrates his S4 powering the TV at something higher than 30Hz. Of course, it might also be a problem with the Qualcomm chipset version of the S4... I may never know...