HSD "transmission"
Also, keep in mind that this car has no "transmission" in the traditional sense of the term. There is no changing of the gear ratios - whatsoever. The car is always in "high gear". It's like getting onto a 10-speed bycicle on it's highest gear.
The engine alone cannot get the car rolling from stop. There simply is not enough torque. This is why traditional cars have transmissions, and lower gears - to provide more torque at a lower speed. However, the HDS also has at its disposal the MG2 generator-motor. Luckily for us (and the success of HSD), MG2 is most efficient at lower speeds. Therefore, the MG2 motor is what does most of the work propelling the car from standstill.
The planetary gears, or power split device, is hard-coded to deliver the power at a fixed rate. It cannot change. There are three variables - ICE, MG1, and the drivetrain (which is MG2 and the wheels). I don't have the formulas in front of me, but approx 75% of the engine's toque is delivered to the drivetrain. From stop, this wouldn't get you far. But approx 25% of the torque is driving MG1; and since the car is not moving, all the power is channeled to MG1. This generates electricity. This electricity is used to power MG2 to propel the car. And once it starts running, power is also being delivered directly from the engine via the power split device as well, supplementing MG2.
Whenever one of the variables is zero (engine stopped, or car not moving) - then the math through the power split device is quite simple. This is why the engine can never run when moving faster than 42MPH. This would cause the MG1 motor-generator to spin faster than is spec'd to do so. Even in "neutral", rolling down a hill with the engine off - MG1 will spin. The transmission is always engaged, and never changes ratios.
So, while there may always be arguments as far as which is the best power source to use and when, just keep in mind that the power distribution is fixed, and follows very specific rules. Even in the case of "Electric Only" mode, MG2 supplies the power, directly to the drivetrain. However, the power split device is still engaged, and still spins - usually the MG1 motor. (It can be set to spin freely, not supplying or wasting energy). Spinning the motor is less efficient, and is done only when necessary - not supplying fuel to the cylinders saves fuel, but still requires energy from the system (acting as an engine brake) - but usually at those speeds, the engine is running, powering the drivetrain, and generating electricity for either storage, or supplemental power to MG2.