It does not matter if you have "too many" amps. Each device will only take what it needs.
Under NO CIRCUMSTANCES should you draw power for your motors from the Arduino board.
Just connect all your motor drivers in parallel to the power supply. You can also draw power for the Arduino from the power supply.
You have not provided a link to the datasheet for your stepper motors. You may find that a voltage higher than 12v would be better for driving the motors.
Stepper Motor Basics
Simple Stepper Code
Pardon me if you already know this, but it seems you may not. Pardon the analogy, too. If you hang all your socks (ie, motor drivers or other loads) on a clothesline (power supply) to dry they're all in parallel connected to the line. Think of the clothesline as Vdd. As long as the clothesline is strong enough to support the load (current capacity) without snapping you're OK.
On the other hand, if you connected one sock to the line and another to the free end of that one and so on, they'd be connected in series.
Thank you for your replies, they are very insightful :).
I'm more of a software guy which is why I'm clueless when it comes to this :p.
The motor specs are as follows:
3.2V 1.2A 1.8/step
The power supply I have is 12V 30A.
Am I understanding you correctly in that this is how I should wire the PS?
Shouldn't there be a 12V -> 5V converter before going to the Arduino?
(the ground wire on one of the drivers is missing, but is there in reality AND there is no red wire from the PS into the 5V pin on the arduino, excuse me)