Final answer:
The assertion about the centromere nucleating an aster is false; it is actually the centrosome, containing centrioles, which organizes the microtubules into a radial array called an aster during mitosis.
Step-by-step explanation:
The statement that the centromere nucleates a radial array of microtubules called an aster is false. The actual structure that nucleates microtubules and organizes the radial array known as the aster is the centrosome, not the centromere. The centrosome contains a pair of centrioles, each a cylinder made up of nine triplets of microtubules, and it functions as a microtubule-organizing center in animal cells. During the prophase of mitosis, the centrosomes move to opposite poles of the cell and from there, they nucleate microtubules that grow towards the middle of the cell to form the mitotic spindle, which will eventually be involved in separating chromosomes.