Final answer:
The paired structures composed of tubulin that play a role in eukaryotic mitosis are known as centrioles, which form part of the centrosomes responsible for organizing the mitotic spindle.
Step-by-step explanation:
The paired structures composed of tubulin that play a significant role in eukaryotic mitosis are known as centrioles. Specifically, the mitotic spindles arise from cell structures known as the centrosomes, which consist of pairs of centrioles. The spindle fibers, which include kinetochore microtubules, extend from the centrosomes to aid in the separation of chromosomes during cell division. The centrosomes, each having a pair of centrioles, move to opposite poles of the cell during prophase. As they move apart, they help organize the microtubules that will become the mitotic spindle.