Final answer:
The described stage is metaphase, the second phase of mitosis where chromosomes line up at the metaphase plate and spindle fibers attach to the centromeres, preparing for sister chromatids to separate.
Step-by-step explanation:
The stage being described where the spindle grows, attaches to chromosome pairs at the centromere, and chromosomes line up at the metaphase plate in their most condensed state, is known as metaphase. This stage is the second phase of mitosis, during which the chromosomes become maximally condensed, and sister chromatids are lined up at an equatorial plane in the middle of the cell. The kinetochores on the chromosomes attach to the microtubules of the spindle, ensuring the sister chromatids will be separated and moved to opposite daughter cells during cell division.