[Galaxy S III Accessories] a32quaeler:
Your drawing No 1 is what I use (see below). No 2 is how it should be indeed (but where is the "modded cable" coming from?). While No 3 will not help you since only the presence of a shortened HDMI-CEC pin (+ opening the display a bit) will power ALL the USB-ports including U1+U2 (that activity mode of the Lapdock is indicated by a small white LED next to the touchpad) - so there is no "pre-power" available. But (again) anything that provides that ground contact on the HDMI-plug will do the trick... I actually have one 90degree HDMI-adapter (don't know how to call it in English), which does exactly that and shortens those pin(s) and simulates to the Lapdock the presence of a device (I assume that is NOT on purpose but it works with a second, identical adapter as well). Don't take me wrong you do not need that one if you conect a device (any) directly to the microHDMI-to-HDMI adapter but it is needed when you use HDMI extension cables (etc.) that do not pass all wires to the HDMI device.

I attached some pics how I wire that thing. Pic 1: the micro HDMI plug on the Lapdock is turned by me by 180deg just to make a bit more room for the microHDMI(fem)toHDMI(male)-adapter. You may directly attach the dongle to it (it is relatively stable and easy to carry around - pic 2). That's what one could call "entertainment mode" since you may want to watch videos etc. this way. But than you have not enough space for the microUSB-cable for kb/mouse. That is what I use the 90deg-adapter for. This adapter alone signals already the Lapdock to power up (no other HDMI-cable or adapter I own does this). Back to pic 1: The microUSB(fem)-to-microUSB(male)-cable has the red 5V wire cut. The microUSB-to-USB + USB-microUSB-OTG(!) adapter is there only to signal the OTG-host mode for the S3. The stuff on the right are things you may use on the free USB-port.

That strange device with the mobile speaker attached to its headphone jack has to be explained: it is a (5 Euro) "USB sound card". That is a bit odd... the Lapdock has stereo speakers which are working well (but not great) and the audio-output via HDMI(cast) to the Lapdock works perfectly (sound is ok and in sync when watching videos & you can control volume etc. from the S3 or the Lapdock keyboard) but the allshare cast SW on the S3 does not allow you to plug in a headphone or connect a bluetooth audio-device to the S3 for output of the video(!)-sound. You can use headphones for mp3-player music while using an HDMI display etc. but when you switch on a video you have to remove headphones otherwise the allshare connection stops. There might be two reasons 1: HDCP, 2: there is a small lag in video display from the wireless transfer protocol and the audio stream is equally lagged on purpose to be well in sync with the video stream. You may want to bypass that artificial restriction because the Lapdock has NO headphone jack ... and you can by using such a "soundcard" which is fully supported by the S3 but the sound is then indeed a bit "in advance" of the video stream.

Less exotic devices you can attach are external disks/pen drives or even game controllers (all of them work)... Pic 3 shows you how I wire it for "productivity mode" :)