Final answer:
Microtubules are the cytoskeleton elements that are longer, thicker, and organized near a centrosome, and they serve various functions including maintaining cell shape and facilitating chromosome movement during cell division.
Step-by-step explanation:
The cytoskeleton component that is longer, thicker, and organized near a centrosome at the nucleus is the microtubule. Microtubules are hollow cylinders made up of alpha and beta-tubulin polymers and are the largest structures within the cytoskeleton, with a diameter of approximately 25 nm. They are crucial for maintaining the cell shape, aiding in organelle movement, chromosome segregation during cell division, and forming structural components of cilia and flagella. In comparison, actin filaments and intermediate filaments play different roles in the cell, such as providing mechanical support, facilitating cell movement, and bearing tension, respectively.