The kinetochore anchors chromosomes to microtubules in the spindle during cell division. The centrosome serves as a nucleating center for microtubules in the spindle and anchors them to opposite sides of the cell.
Metaphase is when chromosomes attatch to spindle fibers in the phase of mitosis.
During metaphase each chromosome attaches to spindle fibers. The centriole anchors the spindle fibers and helps in splitting the chromosome.
Spindle
During mitosis a double-stranded chromosome attaches to a spindle fiber centromere.
prophase
Spindle fibers
Chromosomes attach to the mitotic spindle during the metaphase of mitosis. Part of the answer depends on how you define the stages of mitosis and not everybody does this the same way. The short answer is all of them.
The answer is telophase.
Spindle fibers attach to chromosomes during mitosis. Specifically, they do so in the metaphase portion of mitosis, in preparation for the splitting of the cell.
The cellular component that helps pull apart the chromosome in mitosis and meiosis are the spindle fibers. These spindle fibers are made of micro-tubules.
Prophase