In most large firms, market makers (we simply call them traders) are assigned by sector. Generally, a new market maker will have anywhere from 10-20 stocks, maybe 5 very illiquid, barely traded ones, 10 low volume ones, and 5 or so medium volume ones. The reason for which they are divided by sector is so, if news comes out affecting the sector, they can auto-adjust all quotes at once. Most mm's start trading a group of roughly 20 very low to medium liquidity bank stocks, which they can ease into, get a feel for, and keep fair and orderly markets in during FOMC meetings, etc. Good practice.
Now...for the big stocks like MSFT, INTC, DELL, etc., there would generally be one mm/trader with as many as three assistants. Thats right; for a NASDAQ 100 stock or, for example, in anticipation of earnings of an internet stock, there is generally one trader who is the subject matter expert and who only follows that issue. He or she has assistant traders (people on their way to trading bank stocks, as mentioned above) around him to grab the phone, check stock loan and borrow, monitor news and inventory, maybe handle the flow when he goes to the bathroom, etc.
That's my experience, though I have never made markets.
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