High Amp Question

I just recently swapped the stock alternator to a 135 amp one, but I was then told that I also needed to swap the cable that goes from the battery to Alt if I wanted to see a difference. I swapped it with a 4 gauge, but I wasn’t sure of which one of the two cables connected to the battery belonged to the Alt (thin or big). So I just connected the 4 gauge wire directly to the battery without disconnecting the two that were already were there. I just want to know which one is the cable I can disconnect at the battery and if its even necessary to disconnect (will it draw electricity from the battery even if disconnected at the Alt)?

Thanks in advanced!!!

The two cables at the batt. pos.(+) post are batt. to starter motor, [thick one] and batt. to engine bay fuse box, [thinner one], the alt. lead should also run to the engine bay fuse box, not the batt. 94