Most common mobo fan headers can supply up to 1.0 A total load. The High-Amp header on that mobo can do up to 3.0 A load. Those limits apply to EACH header separately.
Splitters and Hubs are different devices, BUT the way they are labelled at many points of sale (including on-line) is never consistent, and often wrong in my opinion. I'll get to the difference in a moment, but first a common feature of both items. Any fan header can accept the speed signal (two pulses per revolution) coming back to it from ONE fan for counting. You cannot send more than one fan's speed signal to a mobo header, or it causes enormous confusion, wrong readings, and sometimes bad error messages. So, any decent Splitter OR Hub will send back to its mobo fan header the speed signal from only ONE of its fans, and ignore the rest completely. You will never be able to "see" the speeds of those "other" fans. However that has NO impact on ability to control, because the system does NOT care what the fan speeds really are. In fact, the control of fan speeds is based on TEMPERATURE measured at an appropriate sensor, and all of the fans connected together on a Splitter or Hub will receive the SAME control signals. IF all the fans are identical, they will all run at about the same speed; if they are different models, their speeds will be different, but that does not matter to the control system. It is only trying to force enough air flow to keep a TEMPERATURE on target. Where is does natter, though, is FAILURE detection. A mobo fan header monitors the speed of its fan and will send out a warning if there is no speed, assuming that the fan has failed. But if not all of your fans' speed signals can be sent back to a header, those fans cannot be monitored for failure. It is up to YOU to check them all once in a while to ensure they still are working. This also means that, if you use one of these devices, you must connect one fan to the particular output port that DOES send a speed signal back to the mobo, or it will cause a fan failure error message.
One more bit of background - the difference between fan types. The older 3-pin fans are controlled by varying the voltage supplied to them on Pin #2 from +12 VDC max down to about +5 VDC min. Any less voltage and the fan may stall and not re-start until the voltage is raised significantly. (Pin #3 carries the speed pulse signal back to the mobo header). 4-pin fans always receive a full +12 VDC from Pin #2, and also receive the new PWM signal on Pin #4. Inside them they have a small chip (3-pin fans do not have this) that uses the PWM signal to modify the flow of current from the +12 VDC supply though the motor windings to achieve speed control. What happens if you mis-match the fan type with the header Control Mode? If you plug a 4-pin fan into a header using Voltage Control Mode the fan never receives a PWM signal and cannot modify the incoming power. BUT that power is not a fixed +12 VDC; it VARIES and thus CAN control the fan's speed. The other mismatch is a 3-pin fan connected to a 4-pin header that actually is using PWM Mode (some can be set not to). The fan receives a full 12 VDC constantly on Pin #2 and does not receive the PWM signal (it can't use it anyway, because it has no special chip), so the fan runs full speed all the time, You get good cooling, but no control.
Now, the difference according to me. A SPLITTER is a simple device that connects all its fans in parallel to the power supply (+VDC on Pin #2, and Ground on Pin #1) so that they all share the same supply. In the case of 4-pin fans, that PWM signal from the mobo also is shared to all the fans, but this signal is not subject to max current limits. Thus, the only source of power for all the Splitter's fans is from the mobo header, and is limited to 1.0 A max (or 3.0 A for the special high-power header). A HUB is different because it also has a direct connection to a power output from the PSU which has a much higher current available than a mobo header does. The Hub draws all power for the fans from this source and does not connect any fan to the mobo Pin #2 source. So a Hub can power and control many more fans than a mobo header can using a Splitter. BUT that power source is ALWAYS +12 VDC. So, the only way to exercise CONTROL of the speed of fans via a HUB is if they are all 4-pin fans, and the Hub is connected to a mobo header that actually is using PWM Mode for control so that it can supply the PWM signal for the Hub to share out to its fans. (There are one or two exceptions to that rule because of unique designs.) Thus, a HUB cannot control any 3-pin fan's speed.
SPLITTERS come in at least two physical forms. One appears to be just a collection of wire "arms": one ends in a female (with holes) fan connector that plugs into the mobo header, and the others all end in male (with pins) connectors to plug your fans into. The other looks like a simple printed circuit board with one cable going to the mobo header, and several output ports of pins. HUBS come in both those forms plus a third: a box with TWO cables out and a bunch of output ports in the box.
How do you tell which is which if the labels are wrong? The big clue is that a HUB has a special third cable that ends in a connector that MUST plug into a power output (either 4-pin Molex or SATA) directly from the PSU to get all the power for the Hub's fans. A Splitter does not have this "arm" so all its fans draw power from the mobo header only.
These days, it is hard to find a Splitter in the 3-pin design, but that does not matter. The physical size and electrical layout of these connectors is the same, so you CAN use a 4-pin Splitter with either type of fan and header just fine. Of course, for 4-pin fans you MUST use a 4-pin design.
So, IF you have 3-pin fans then you MUST use them with a mobo header that can be configured (MAY be this way anyway) to use the older Voltage Control Mode (aka DC Mode) to control the fan's speed. To connect more than one such fan to a header, you MUST use a SPLITTER because this fan type cannot be controlled in a 4-pin fan Hub system (excepting the very few odd Hubs). Then the Splitter and its fans are limited by the mobo header's max current capacity, normally 1.0 A but on some 3.0 A.
IF you have 4-pin fans, you can use either a 4-pin Splitter or a Hub to connect several to a single mobo fan header as long as it IS configured to use the newer PWM Mode for control. IF you choose a Splitter then the group is subject to the mobo header's current limit; IF you choose a HUB, then that limit will not apply.
The ASUS Fan Extension header is for use with an optional (and sold separately) Extension Card that adds three extra fan headers that each perform like a common 1-Amp mobo fan 4-pin header.