A stone is released from an elevator going up with an acceleration of g/2. What is the acceleration of the stone just after release?...

As the stone is still travelling on the elevator there are two forces acting on it at the same time:

1. The force from the elevator to the stone,
2. The gravitational force.

The moment the stone leaves the elevator it becomes a free object and the force of the elevator stops and the only force that is acting on the stone is the gravitational force. 
Now we know that W = mg, the acceleration felt by the stone is g and it will be in downward direction.