B757 Captain reports a near collision with a B737 during taxi at the juncture of Taxiway's P and N at MIA.

Narrative

[We had a] near collision on taxiway. Ground issued us a sequence to follow an Air Carrier. We were on Taxiway N taxing to Runway 08R and to monitor the Tower. Air Carrier X was on Taxiway P; behind the fire station. I had a visual on the Air Carrier and I did not see any other traffic behind him. I stopped short of Taxiway P to allow the Air Carrier to pass ahead of us. He got a clearance to taxi into position and was cleared for take-off. I started to taxi to follow him. I cleared my left side and saw no traffic. Shortly after I started and well into my taxi; to position us #1 short of Runway 8R; I heard the Tower with a tone of urgency calling Air Carrier Y; with no response. I sensed that something was about to happen so I stopped. I believe by stopping we avoided a major ground collision. Air Carrier Y was passing at my 8 to 9 o'clock position at high taxi speed; estimating it to be well above 20 to 30 KTS. I have no doubt that his wing would have impacted the cockpit if we had not stopped. I don't know how he missed our left wing; his right wing appeared less than 20 FT in front of us. I strongly believe that Air Carrier Y may not have seen us at all; and his taxi speed may have been excessive. Someone was looking out after us. We avoided a major accident.