The component trail inside of the PSU that is responsible for producing the different voltages are called rails. You really don't have to be worried about how the 3.3V and 5V power is derived, because pretty much all of the ways to produce those outputs is good enough on a modern PSU.
With the 12V output, there can be multiple true rails, which for the most part will only be on the very high voltage PSUs. On most PSUs though, there is only one physical rail. This rail can either be left as one large unit, which will have a physical limit to how much current it can handle, and will usually also have a safety measure called over current protection which keeps it from drawing a damaging amount of current.
OR that big rail can be split up with over current protection into multiple different units. Reason this is done is that the individual wires can only handle so much current before they start to overheat and melt their insulation and cause damage. With this way, each division will have a set limit, but collectively they are also limited by the single rail they are split from. Manufacturers will then need to be smart in how they arrange the different power connectors on those splits. If you buy a well reviewed quality power supply, you the end user do not have to worry about it, unless you plan to run a very powerful TEC cooler.
Let's take the BFG ES-800 as an example.
It has a single large rail divided up with OCP into 4 separate units.
12V1 22A ATX 24pin connector, Molex and SATA connectors
12V2 22A CPU connector
12V3 36A 6 pin PCI-E and 8 pin PCI-E
12V4 36A 6 pin PCI-E and 8 pin PCI-E
Combined limited to 65A
12V1 has 264W available ATX connector only has 2 12V wires, so it won't be pulling much current from the 12V output. You can have a fair amount of fans and hard drives running from the molex and SATA before you get near 200W.
12V2 also has 264W, that is all for your CPU
1V3 and 12V4 both have 432 Watts available. Both of them have a single 6 pin and single 8 pin PCI-E connector. 6 pin connectors on a normal videocard should pull no more than 75W and the 8 pin no more than 150W. So 225W combined. Those rails won't shut you down until you hit 432W, even if your videocard is highly overclocked and pulls the PCI-E connectors out of spec, you have more than enough power available.
So let's say you are pulling 60W from the ATX 12V wires, 75W from the peripheral connectors. 12V1 135W, or 11.25A
CPU is using 175W 14.6A
HD5870 on 12V3 using 120W or 10A
HD5870 on 12V4 using 120W or 10A
Total of 550W or around 46A
None of the components it drawing their unit to the limit and all together they are not drawing the total to the limit.
Let's figure you have a highly overclocked processor, a couple of HD5970s a bunch of hard drives and fans.
12V1 with ATX and all those HDDs and fans 190W 16A
12V2 highly overclocked CPU 220W 18.3A
12V3 OCed HD5870 200W 16.7A
12V4 OCed HD5870 200W 16.7A
Total 810W or 67.5A
None of those individual units is close to the limit, but all together they are over the 65A limit of the entire system.
Let's go back to the first example, but your motherboard has a short at the ATX connector that keeps the power draw increasing.
12V1 264W and short wants to keep drawing more. 22A
12V2 175W 14.6A
12V3 120W 10A
12V4 120W 10A
Only 56.6A total, so it doesn't meet the 65A limit, but 12V1 is already at its individual limit, and if the OCP doesn't shut off the PSU, it will keep climbing and will melt the wires on the ATX connector and cause further damage.
Biggest point to come away with on this is buy quality, look at competent reviews and you won't have to worry, unless you have a very non-typical setup