to get or take control of something and keep it exclusively to/for oneself;
e.g. He didn't want to monopolize the debate, preferring instead to hear his opponent.
(verb)
to take or occupy the largest share or position of something, especially, as a business, to gain complete control or possession of a commodity, service, or trade;
e.g. Large brands monopolize the shopping space in many malls. There are a couple of companies that monopolize the market for sodas.