Thanks for those details. I could not find a manual for the be Quiet Silent Loop system, but I found enough info to figure this out. The design is as I suspected - the pump is supposed to run full speed all the time, and control of the CPU temperature is done by having the CPU_FAN header control the two fans on the radiator. Further, the FANS are of the 4-pin PWM type, and the PUMP has a 3-pin connector. The info on the Intel DQ77MK mobo says it has one CPU_FAN header and two case fan headers; all of these are 4-pin type using only the new PWM Mode of control. That suits your needs just fine.
One type of info missing, however, is the current consumption (amperes) required by each fan and the pump. Typically such a fan might use 0.1 to 0.2 A each, and the pump less than 0.5 A. The limit to be met is that a single mobo fan header can supply up to 1.0 A total current. So, IF my guesses about amp ratings of the pump and fans are correct, it IS acceptable to connect all three devices to the CPU_GAN header with appropriate wiring. HOWEVER, if you can find Amp ratings on each fan AND on the pump unit, add them up. IF you can confirm that the total does not exceed 1.0 A, you can connect this way. BUT if the total exceeds 1.0 A, OR if you cannot find any such info and are worried about that limit, I will suggest at the end another way to make connections.
So, first plan for connecting ALL THREE devices to the CPU_FAN header IF the total current load does not exceed 1.0 A. You already have one Splitter so you can connect both fans to a single header. You will need one additional simple 2-putput Splitter similar to what you have, but do NOT get a Hub. A HUB is different and it always has a third type of cable "arm" that must plug into an output connector from the PSU. So, with the added Splitter, plug that into the CPU_FAN header. Now, look at that Splitter's two outputs, and one of them will have all four pins in it, while the other is missing Pin #3. Plug into the one with ALL FOUR pins the cable from the PUMP that ends in a 3-pin connector. This will ensure that the PUMP's speed signal is sent to the CPU_FAN header. That header pays special attention to the speed signal of its "fan" (in this case, the pump) to monitor it for FAILURE that might cause rapid heating of the CPU that could damage it. In an AIO system, it is failure of the PUMP that can cause the most dangerous potential for overheating, so that's the item that needs to be monitored closely. Now, connecting the PUMP's 3-pin cable to a 4-pin header that uses the new PWM Mode of control takes advantage of a quirk of design. Technically, this is a mis-match of 3-pin "fan" (really, pump) to a 4-pin header. That type of mis-match causes the 3-pin device (the pump here) to always run full speed with no ability to control its speed. That is exactly what we want for the pump.
Now, take the Splitter that has the two rad fans attached to it and plug that into the other output from your first Splitter - that is, the one that is missing Pin #3. This has a small impact you need to understand. Any fan header can deal with the speed signal coming back to it from only ONE fan - more causes confusion and wrong readings. So in fact a Spltter will only send back to its mobo header ONE of its fans' speeds and ignore the others. This means you can never "see" the speeds of the "other" fans. In the arrangement I suggest here, the ONLY speed sent back to the mobo CPU_FAN header is the PUMP speed (so it can be monitored for failure). The speeds of BOTH rad fans are NOT being sent anywhere you could measure them, so you will never know what they are. You CAN observe them and see that their speeds change as workload and heat change, but you won't see any number for their speed. This also means that there is no way for your mobo to warn you if those rad fans fail, so YOU will need to check them once in a while to be sure they both are still working.
If you do as I suggest there, your pump unit will always run full speed as designed AND it will be monitored for failure by the CPU_FAN header. Both fans on the radiator will have their speeds automatically controlled by the CPU_FAN header according to the actual temperature measured inside the CPU chip. And the two other CASE fan headers on your mobo (controlled by a mobo temperature sensor) will be available for case fans.
OK, PLAN #2 - IF you find that the total current for the pump plus two rad fans is over 1.0 A, or IF you are worried about that. The alternative is to keep the two rad fans together using the Splitter you have, and connect that to the CPU_FAN header so that their speeds are controlled automatically according to the CPU temperature. Then you need to use one of the two other fan headers (intended for case ventilation fans) to power the PUMP only. If you plug the pump into one of those, it WILL run full speed as intended. Usually such a header also monitors its "fan" (the pump in this case) for failure and will give you a warning message if it does fail. However, the case fan header will NOT take automatic drastic action to shut down your system when that failure happens - YOU will need to shut down quickly if you ever get a warning that the "case fan" that really is your PUMP has failed. This arragnement leaves you with only ONE fan header to use for actual case ventilation fans, but that's not really a problem - using a Splitter or two you can connect at least threee standard case fans to a single header. You just have to pay attention to the 1.0 A limit for that header.