Why did the crashed TAM Airlines Flight 3054 veer off the runway only near the end?
Right Engine thrust

The engine takes about 12 seconds to spool up from idle to full thrust. 

Auto-throttle had held both engines near idle during the approach to touchdown. The throttle levers should both be retarded from "climb" to "idle" position prior to touchdown. But only in the last two seconds before touchdown, after the aircraft emitted a warning, was the left throttle retarded - but the right throttle lever was not moved from the "climb" position.

When the left throttle lever was retarded, this disengaged auto-throttle, so  the right engine started to spool up to "climb" power setting as commanded on the right throttle lever.

So immediately after landing the right engine wasn't producing any thrust. 

The thrust only developed gradually during the following 12 seconds as the aircraft traveled down the runway.

Rudder authority

At landing the aircraft might be travelling at 140 knots. At this speed, deflection of the rudder by the pilot can still have significant effect and can counteract asymmetric engine thrust.

As the aircraft traveled down the runway, airspeed would have reduced and rudder authority gradually diminish at the same time as the right engine was spooling up to CL (climb) power.

The aircraft ran off the runway at about 90 knots.

Nosewheel steering

When using the rudder pedals for nose wheel steering, the steering angle starts to reduce at 40 knots and progressively reduces to zero degrees at 130 knots.

According to the accident report,


  When the accident happened, the volume of precipitation was 0.6 mm. 


So a combination of speed and a wet runway may have reduced the effectiveness of nosewheel steering.

I don't know, but I suspect that nosewheel steering may not be able to fully compensate for the yawing effect of left engine at idle and right engine at climb power.

Differential braking


  The FDR also recorded the use of the rudder and the differential braking by the pedals as the aircraft veered to the left (probably in an attempt to maintain the plane on the runway and stop it). 


It seems that the crew really needed to shutdown or idle the right engine to complete a landing within the boundary of the runway.