This work deals with some numerical experiments regarding the distributed control of semilinear parabolic equations of the type y* -y~ + f(y) = uX.,, in (0, 1) x (0, T), with Neumann and initial auxiliary conditions, where w is an open subset of (0, 1), f is a C 1 nondecreasing real function, u is the output control and T > 0 is (arbitrarily) fixed. Given a target state YT we study the associated approzimate controllability problem (given e > 0, find u 6 L2(0, T), such that Ily(T; u) -yT [[L2(O,1) < c) by passing to the limit (when k --~ oo) in the penalized optimal control problem (find uk as the minimum of Jk(u) = 1/2 [[uH22(0,T)+ (k/2)]]y(T; u) -yTll~2(0,1) ). In the superlinear case (e.g., f(y) = ly]n-ly, n > 1) the existence of two obstruction functions Y=~oo shows that the approximate controllability is only possible if Y-oo(x, T) <_ yT(x) < Yc~(x, T) for a.e. x E (0, 1). We carry out some numerical experiments showing that, for a fixed k, the "minimal cost" Jk(u) (and the norm of the optimal control uk) for a superlinear function f becomes much larger when this condition is not satisfied. We also compare the values of ./k(u) (and the norm of the optimal control uk) for a fixed YT associated with two nonlinearities: one sublinear and the other one superlinear. @