It is based on a combination of branching and divergence. Most old books on palaeontology were based on this paradigm. Admitedly, Evolutionary Systematics suffers from a number of shortcomings. This the site that I got the kewl icon at the top of ths page from. Why I prefer Evolutionary Systemmatics Granted Evolutionary Systematics has problems, as does any conceptual system.
Deep time means time extending over millions of years.
This is part of the vastness of the universe - the temporal vastness that goes alongside the spatial vastness. We can't see plants growing - it is too slow. But if things were speeded up the astonishing metamorphosis would be visible. It's the same with evolution. Evolutionary systemmatics is a means of describing this process.