Even though black hole scalarization is extensively studied recently, little has been done in the direction of understanding the dynamics of this process, especially in the rapidly rotating regime. In the present paper, we focus exactly on this problem by considering the nonlinear dynamics of the scalar field while neglecting the backreaction on the spacetime metric. This approach has proven to give good results in various scenarios and we have explicitly demonstrated its accuracy for nonrotating black holes especially close to the bifurcation point. We have followed the evolution of a black hole from a small initial perturbation, throughout the exponential growth of the scalar field followed by a subsequent saturation to an equilibrium configuration. As expected, even though the emitted signal and the time required to scalarize the black hole are dependent on the initial perturbation, the final stationary state that is reached is independent on the initial data.
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