What structures of the nucleus of a eukaryotic cell play a major role during its division?

What structures of the nucleus of a eukaryotic cell play a major role during its division? Due to what in nature there is continuity between generations of organisms?

The nuclear apparatus of eukaryotic cells has a number of differences from prokaryotic ones. Firstly, the DNA-containing component is separated from the cytoplasm by a special membrane (nuclear envelope), secondly, the amount of DNA in the nuclei of eukaryotes is thousands of times greater than in the composition of bacterial nucleoids, and thirdly, the DNA of eukaryotes is a complex nucleoprotein complex that forms a special structure – chromatin, of which eukaryotic chromosomes are composed. Further – the composition of the nuclei of eukaryotes includes several physically unconnected chromosomes, each of which contains one linear giant DNA molecule. Each chromosomal DNA is a polyreplicon structure, i.e. contains many autonomously replicating chunks.