#nodemcuarduinomosfetpower electronicstransistors
I am working on a project to start a vehicle using Automotive Relays. 
And I am following this circuit in the tutorial to do so. Everything works fine on Arduino UNO. But I want to use ESP32 of this kind in my final project and ESP32 is 3.3v with ~12mA max current. When I plug ESP32 to the above-given circuit (Obviously powering through external 5v connection with the shared ground and not 12v battery), it fails to trigger the relay and instead resets. Any suggestions?
My ESP32 Circuit. 
What are those "larger components"? The only larger thing is the relay, and most relays will fit on a breadboard.
This is how you control the relay (the coil is shown next to the diode), it assumes you can connect the 12V's ground to the Arduino's. Resistor, transistor and diode are normal, small components. This relay is just a few cm long, wide and high. It can switch 10A and 230V. If you tell us more about what you want to switch I can give you more directed advice.
edit re your shopping
The relay requires 90mA from your 5V power supply. That will add a couple of hundreds of mW in the Arduino's voltage regulator. At 12V in that would be 630mW, which is a pity. If you have 12V in it would have been better to use that for a 12V relay.
The TIP31 transistor is overkill. It's a power transistor, and they don't have very high \$H_{FE}\$ (the current gain). Next time go for a TO-92 general purpose transistor like the BC547. The BC547B variant has an \$H_{FE}\$ of minimum 200. Go for a high \$H_{FE}\$. This one is still OK at an \$H_{FE}\$ of 100, but I would take a safety factor, and calculate with 40. Then the base current has to be 90mA/40 = 2.25mA. A 1k\$\Omega\$ base resistor will give you 4.3mA, so that's OK.
Although they are one the same chip, the USB and MCU circuits can function independently. For example, the USB part can be used to reset the MCU part.
Best Answer
The ESP board has 5V in but runs on 3.3V, has a small ldo on the board to regulate the 5V down. And as the output current rises the output voltage level will drop below 3.3V.
The solution is to replace the TIP NPN Darlington transistor with a logic level N-Channel mosfet. IRLZ44 or STN4NF03L maybe. These are voltage driven instead of current driven and won't have the issues with the ESPs limited current and sagging voltage output.
Alternatively, use a opto isolated relay board/module. The esp would drive a small led based optocoupler that then drives a transistor and the relay.
Or use a smaller relay. Or use a small nfet to drive your Darlington transistor. A bunch of options. The logic level mosfet would be the simplest imho.