Is there a name for the following process?

Say I have an absolutely continuous probability density function $f$ with compact support, and I take $k$ independent samples $x_1,\dots,x_k$ from $f$. Then, I let $x^*$ be the sample for which $f(x_i)$ is the largest, i.e. $x^* = \arg \max_i f(x_i)$. My question is, is there a name for this process, and can anything be said about the distribution of $x^*$? This basically has the effect of emphasizing the modes of $f$ more aggressively.