GPUs draw more power when they're working harder. Pretty much, the more instructions, calculations, and pushing around data they're doing, the more '0's and '1's (which are represented by voltages) need to switch places, hence more current flows and waste heat is produced. Also, the higher the voltage, the more power is used.

The listed TDP is somewhere around the expected max realistic power draw if not overclocked, as a kind of guideline as to how much heat the cooling solution needs to handle. This corresponds to some kind of realistic worst-case scenario in terms of workload and thus power draw. In practice the coolers can of course dissipate more than the listed TDP, so there's some leeway. If you overclock, power draw will increase some, since there may be more calculations per second. If you increase voltage, power draw will increase by even more, so you can go well over listed TDP.

There's no way a GTX 560 Ti by itself should be drawing 20A (from the +12V rail) unless it's heavily overclocked, with some voltage increases.

The computer power supply takes in AC voltage from the wall (something like 115V or 230V AC depending on which country you live in and where), filters it, transforms it, and filters it some more so you get +12V DC, +5V DC, +3.3V DC, and -12V DC. There's a fast-acting feedback loop that essentially adjusts how much power is sent over the transformer to the output side in real time, in response to changes in the load drawn by the computer. That is how it can handle a wide range of power draws by a computer, without wasting a whole lot of power if it's not pulling much.

On almost all computer power supplies, there's not much real distinction between +12V rails. They're all generated by more or less the same circuit. It's just that certain wires corresponding to certain plugs, are grouped together for safety purposes, into different rails. There's a separate over-current protection trip point set on each +12V rail, if in fact the power supply has this feature. If the limit is reached--which should only happen if there's an unintentional short--then the power supply should shut off. So it doesn't really matter which rails you're pulling from. For most modern units, the trip points are set such that there's pretty much no way to hook up a computer such that it will exceed the trip point, unless there's a short (in which case you'd want it to shut down).

The listed TDP is somewhere around the expected max realistic power draw if not overclocked, as a kind of guideline as to how much heat the cooling solution needs to handle. This corresponds to some kind of realistic worst-case scenario in terms of workload and thus power draw. In practice the coolers can of course dissipate more than the listed TDP, so there's some leeway. If you overclock, power draw will increase some, since there may be more calculations per second. If you increase voltage, power draw will increase by even more, so you can go well over listed TDP.

There's no way a GTX 560 Ti by itself should be drawing 20A (from the +12V rail) unless it's heavily overclocked, with some voltage increases.

The computer power supply takes in AC voltage from the wall (something like 115V or 230V AC depending on which country you live in and where), filters it, transforms it, and filters it some more so you get +12V DC, +5V DC, +3.3V DC, and -12V DC. There's a fast-acting feedback loop that essentially adjusts how much power is sent over the transformer to the output side in real time, in response to changes in the load drawn by the computer. That is how it can handle a wide range of power draws by a computer, without wasting a whole lot of power if it's not pulling much.

On almost all computer power supplies, there's not much real distinction between +12V rails. They're all generated by more or less the same circuit. It's just that certain wires corresponding to certain plugs, are grouped together for safety purposes, into different rails. There's a separate over-current protection trip point set on each +12V rail, if in fact the power supply has this feature. If the limit is reached--which should only happen if there's an unintentional short--then the power supply should shut off. So it doesn't really matter which rails you're pulling from. For most modern units, the trip points are set such that there's pretty much no way to hook up a computer such that it will exceed the trip point, unless there's a short (in which case you'd want it to shut down).