Final answer:
The mitotic spindles form from the centrosomes, which are composed of centrioles serving as microtubule-organizing centers during mitosis.
Step-by-step explanation:
The mitotic spindles arise from a cell structure known as the centrosome. Each centrosome is composed of two centrioles, which are positioned at right angles to each other and serve as the microtubule-organizing centers during mitosis.
During prophase, the centrosomes migrate to opposite poles of the cell, and the microtubules extend from them, forming the mitotic spindle that plays a crucial role in chromosome separation and cell elongation.