To user achow101, you say that these are not my addresses but those of the exchanges. Have there been any exchanges who have not honoured their promises to withdraw the funds of users? If so, then I believe users must be warned of such possibilities as when I signed up for Poloniex, there was no mention of anything like them controlling my funds. Could you explain how I can own the addresses that I use for Poloniex to secure myself?
Glad that you saw it worked out. Unfortunately, using most online services or exchanges like Poloniex means that you have to give up control over your own funds. As achow explains, the balances you see on your accounts are just database entries on their servers updated as you deposit to and withdraw from their wallets.
I use some of these exchanges, when I want to use my Bitcoins to buy other alts - in reality, I am sending them my bitcoins, and when I perform a trade on their exchange, I am credited with the corresponding amount of altcoins. I only regain control of those alts when I request a withdrawal and they send me those alts to a wallet I control. So... yes, when we used these centralised exchanges, we are sending them our funds for the promise of that they will be returned to us when we make withdrawals.
Currently, there is a way to remain fully in control of your funds while still exchanging, through so-called decentralised exchanges. These are platforms where users offer trades to and accept trades from each other, P2P exchanging/trading. The only issues now are that they are only a few of them with a small userbase, therefore, fewer trades with fewer alts and with less volume, as well as a slightly more complex method of completing trades. You can check out two that I am using now:
1. https://wavesplatform.com/
2. https://xcpdex.com/
There are a few more in development which I hope will give us the same access and volume as Poloniex, Bittrex and others. It will be a long wait, though.