currentshort-circuit
simulate this circuit – Schematic created using CircuitLab
I have trouble finding value for I2 current. Would I1 go through NODE1 down and close the loop, so I2=0, or go to the left from NODE1 so I2=-I1, or split (if we assume that both short circuit wires have no resistance) so I2=-I1/2. All explanations seems to me reasonable but I think only one is correct.
The voltage at A, B, and Vout are all 2.5 volts. Since the voltage at A and B is the same, there is no current through R2 and R3. The voltage at your output is the voltage at A minus the voltage drop across R2, which is R2 times the current through R2, which is zero. 2.5 minus zero is 2.5
your reasoning is correct that the 39 ohm resistor parallell with the wire can be replaced with just the wire. but there are no other parts that only parallel the wire. To elimitate a resistor entirely both ends must be connected to the same node.
from here-on in the solution can be found by making series and parallel combinations.
I re-drew the circuit without the 30 ohm
simulate this circuit – Schematic created using CircuitLab
every path from A passes through a resistor...
it looks like the next simplification is to combine the 8 and the 24, and then combine that with the 4 and then that with the 12... etc.
Best Answer
The question can't be answered from the model you have for the circuit.
If you take the short circuits to be ideal 0-ohm connections, then it doesn't matter which way the current goes. The voltage across the connecion is still 0 V, and the power used by the connection is still 0 W. And there is no way to tell which way the current flows.
If this is meant to represent a real circuit, then you need to include in the model the actual resistance of the "short circuits". Then you can use the current divider rule to determine the current through each path.
For example, maybe one is 1 milliohm and the other is 1 microohm. Then you'd know that about 999 mA flow through the lower-resistance path and 1 mA through the higher-resistance path.