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Re: South China Sea
They don't have to patrol the entire sea. The island outposts are the mid point in a ~500 mile wide channel, allowing them convenient means of setting up sonar nets/listening posts. This enables their patrols to pinpoint and challenge what they deem to be unwelcome visitors.
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Re: South China Sea
There's an interesting viewpoint from the BBC a week or so ago:
http://www.bbc.co.uk/news/world-asia-36574590
The idea is that the claims aren't for china to watch what goes on in the south china sea, but instead to make sure no-one else can. the south china sea certainly is much deeper than the 200 mile exclusion zone, so would provide many more options to get into the wider ocean undetected
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Re: South China Sea
That's probably right. They want to be able to get their subs in and out via multiple routes undetected.
Of course another aspect has to be making patrols of the Strait of Malacca easier. The Chinese economy is massively dependent on exports and Middle Eastern oil which go through that narrow stretch of water.