Final answer:
The centrosome, located near the nucleus in animal cells, serves as the major microtubule organizing center and contains a pair of perpendicular centrioles.
Step-by-step explanation:
The major microtubule organizing center in animal cells is known as the centrosome. This structure is pivotal in cell division and microtubule arrangement. It is located near the nucleus and comprises a pair of centrioles, each being a cylinder formed by nine triplets of microtubules. The centrioles lie perpendicular to each other. During mitosis, they are key in spindle fiber formation and help in maintaining the cell shape by emanating microtubules throughout the cell.