My answer isn't a full one, but that's because I think the answer depends on, at minimum, the country your broker is in, the type of order you place (limit, market, algo, etc.,) and the size of your order.
For example, I can tell from watching live rates on regular lot limit orders I place with my UK-based broker that they hold limit orders internally until they see a crossing rate on the exchange my requested stock is trading on, then they submit a limit order to that exchange. I only get filled from that one exchange and this happens noticeably after I see my limit price print, and my fills are always better than my limit price.
Whereas with my US-based broker, I can see my regular lotsize limit order in the order book (depth of book data) prior to any fills. I will routinely be notified of a fill before I see the limit price print. And my fills come from any number of US exchanges (NYSE, ARCA, BATS, etc.) even for the same stock.
I should point out that the "NBBO" rule in the US, under SEC regulation NMS, probably causes more complications in handling of market and limit orders than you're likely to find in most countries.