Answer: The official term is vegetative propagation and nearly any plant can be divided in the way you describe. Bulbs produce offsets which can be removed and planted on their own. Many plants can be propagated through tip cuttings by taking a 6" length of new growth, removing the lower leaves and dipping the cut end into rooting hormone. And, some plants will root in water. There are many books on the subject and you can probably find tons of websites devoted to plant propagation if you do a search. Best wishes with your new hobby!
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