) want one of my power supplies, just to start off... Instead of giving him one, I want him to understand how it work (like I learned).. For a starter I wanted to make one without a lot of "difficult" components. This means no huge datasheet analysis etc...
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What do you think about this simple design?

The ATX powersupply has it's 0V tied to mains earth.
That means that your supply will not only be not-floating but going up and down slightly above mains earth with the current going through R11.
If you add it between T2 and Vcc you would not have this issue.
I'm not that noobie... It was just one of my first projects and that ATX power supply is just gathering dust over there... I could use this circuit even on an other supply that I'm sure is isolated from the mains earth..No idea if these fan connectors have a specific name but basically they're http://m.ebay.co.uk/itm/PK-OF-10-FEMALE-3-PIN-FAN-POWER-CONNECTOR-BLACK-INC-PINS-/221915379106?_trkparms=aid%253D222007%2526algo%253DSIC.MBE%2526ao%253D1%2526asc%253D20150519202351%2526meid%253D09e21d979910430083aafad8a8bf5d4d%2526pid%253D100408%2526rk%253D3%2526rkt%253D3%2526sd%253D321895248478&_trksid=p2056116.c100408.m2460
You can get then in 2 and 4 pin for PWM fans.
http://www.overclock.net/t/673960/max-draw-on-cpu-fan-header-p35-ds3l#post8543385 drawing 3.7 amp.
http://www.overclock.net/t/500254/max-amperage-for-mobo-fan-header
You can always give it a test.
For the higher current (input/output power) try 6mm spade connectors, as used in washing machines, dishwashers etc etc. The PCB side just has 2 pins to solder in (using a lot of heat).
Alternative is PCB mount terminal blocks, heaps of different versions around.
What do you think about this simple design?
Well you did ask.
and thanks for that
I'm still a student, not a professional, even I make sometimes mistakes...

Have you considered using a Quad op amp instead of 3 separate packages ?
Reason being less pins to solder (14 vs 24), uses less space, perhaps cheaper.
Hello Lovely_Santa. I don't mean to seem rude with my rather short answers/suggestions.
Don't worry we've all been there, multiple times.

Back to your circuit. If you really want 10V output from 12V input I don't think you can do it that way. If you imagine the base of the BD139 shorted directly to the 12V, then its emitter will be about 0.75V below 12V, and the emitter of the 2N3055 another 0.75V below that.
And it gets worse, because when those power transistors are saturated their current gains will be very low, may only 5 or so, which means the driving op-amp would need to supply 100mA at 12V, and that's not going to happen even with a rail to rail op-amp.
The usual way to get around this low dropout problem is to change one of the output transistors to a PNP type, emitter towards the 12V input, collector towards the output. If you think about it now, rather than the op-amp having to reach right up to 12V to turn on the transistors, it now only has to pull down 0.8V below 12V to turn the transistor on.
In practice because the op-amp won't reach right to to 12V to turn the transistor off, - you need a 2 resistor divider between the op-amp, base of the transistor, and the 12V line.
Just to give you some future ideas Lovely_Santa,
A very rough output circuit, - in practice you'd have to do many calculations or simulations, and more components, before building it.
By using 1 PNP you no longer have 2 base-emitter junctions in series with the 12V, so save 0.7V, which is a very useful amount when you've only got about 2V spare headroom to play with.
By using the op-amp output the other way up you no longer have to find an op-amp that goes right up to the 12V, just up to about 9.5V(output off), and down to about 1V(output hard on). Because you're inverting the sense of the signal here, you use the op-amp +/- inputs the other way around so that the overall feedback is still negative.

Harder to keep stable at all output current levels
) Or the other solution is to limit the output to only a good 7.5V instead of 10V... It don't need to be perfect either... remember that it's just for my brother as a starter...
...
This is becose the p-type material in the transistor is much thinner than the n-type, with that reason the electrons will be less controlable floating from the emitter to the collector... That's what is causing the unstability...
... you have added at lot more gain into your loop.
This seem very similar to my own design but for a beginner's linear regulator I think this design is a bit of overkill, using op amps and all. You can actually make full use of the -12V rail from the ATX power supply for your op amps by the way.

I think it's mostly what mikerj said, because with the darlington NPN NPN arrangement the voltage gain is only about 0.9, so it's stable. When you swap the first TR for a PNP you're sticking about 30+ voltage gain where it's not needed. You can reduce the PNPs unnecessary voltage gain by putting a small resistance in it's emitter, but then start to lose the 0.7V you gained in volt drop across that resistor. Although you keep nearly all the gain of not needing an op-amp that goes right up to the supply rail.
Everything is compromise somewhere or other.
now I don't know anymore what I want
This seem very similar to my own design but for a beginner's linear regulator I think this design is a bit of overkill, using op amps and all. You can actually make full use of the -12V rail from the ATX power supply for your op amps by the way.Then I would need a +-12V OpAmp... I could use it.. but it's useless... becose they will go rail to rail already... + I have a voltage drop over the current resistor... So it would only get a 3th connection in the system...
I sort of agree on the stability of the output TRs.
PNP TRs seem to be not quite as good as NPNs, slightly lower gain and speed, I think it's mostly imagination, when I was very young there were only PNP TRs.
I think it's mostly what mikerj said, because with the darlington NPN NPN arrangement the voltage gain is only about 0.9, so it's stable. When you swap the first TR for a PNP you're sticking about 30+ voltage gain where it's not needed. You can reduce the PNPs unnecessary voltage gain by putting a small resistance in it's emitter, but then start to lose the 0.7V you gained in volt drop across that resistor. Although you keep nearly all the gain of not needing an op-amp that goes right up to the supply rail.
Everything is compromise somewhere or other.
All voltage rails are available at the main 20/24-pin plug. Quite a few common op amp can work with a +/- 12V power rail, like TL084.
)