Just as an aside, even if you had 100% of mining you couldn't spend peoples coins. You could stop people spending their coins, but miners can't modify existing transactions, just not include new transactions in blocks they mine.
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Somewhat related: If someone steals your Amazon credentials, he can use them to mine bitcoins. Using the CPU to mine bitcoin is not efficient and the value of the mined bitcoins will be much smaller that the cost of electricity and Amazon services, but it doesn't mater because he is not paying the bill. For example read: http://www.securityweek.com/how-hackers-target-cloud-service...
PS: It may be a interesting to know this as a theoretical question. But as a practical question, the idea is not profitable at all.