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We investigate in this paper the properties of some dilatations or contractions of a sequence ( of -optimal quantizers of an ${ℝ}^d$-valued random vector $X\in L^r\left(\mathbb{P}\right)$ defined in the probability space $(\Omega ,𝒜,\mathbb{P})$ with distribution ${\mathbb{P}}_X=P$. To be precise, we investigate the -quantization rate of sequences ${\alpha }_n^{\theta ,\mu }=\mu +\theta ({\alpha }_n-\mu )=\{\mu +\theta (a-\mu ),a\in {\alpha }_n\}$ when $\theta \in {ℝ}_{+}^{☆},\mu \in ℝ,s\in (0,r)$ or ∈ (r, +∞) and $X\in L^s\left(\mathbb{P}\right)$. We show that for a wide family of distributions, one may always find parameters (θ,µ) such that ( is -rate-optimal. For the Gaussian and the exponential distributions we show the existence of a couple...