If China went into a recession, it would adversely affect other economies.
China's economy is primarily based on exports. But, as one of the largest economy it is still a significant importer, especially of raw materials. If China went into a recession, global commodity prices and demand for commodities would probably fall. This would be bad for economies like Australia and Canada which produce significant amounts of raw materials.
If China went into recession, there would be an adverse effect on world trade. China would buy less imports and this would lead to a slowdown in global trade. It could also have a significant effect on global confidence, causing sluggish global growth.
I was interested to recently learn that the UK exports twice as much to Spain as it does to China. Therefore, we might expect a recession in China to have limited effect on UK economy. But, the Chinese economy is such an important influence on global economy that the UK would be effected indirectly.
There are also a few uncertain outcomes. For example, in a recession, would China still have a large current account surplus? (you would expect the surplus to remain). In that case, China may continue to buy dollar assets and it would have an incentive to try and keep its exchange rate low.
- It depends why a recession in China occured? - was it due to a collapse in external demand or due to a tightening of Chinese Monetary policy.
- Would the recession affect other Asian countries as well?
- A recession may well heighten trade tensions and could lead to a rise in protectionist sentiments.
Impact of Chinese Recession in ChinaThe biggest concern over a recession in China would be the impact on China itself. The transition from a rural economy to an urban economy has been so swift that it has been estimated that China needs a growth rate of 7.2% to prevent a rise in unemployment.  Negative growth could have a devastating effect on Chinese society - where there is little if any unemployment insurance.
Chinese Economy vs US EconomyIf Chinese GDP fell, the US may gain a bigger share of world GDP; therefore it may be doing relatively better than China. But, a recession in China would damage the absolute living standards in the rest of the world.
How Likely is a Chinese economic Collapse?
I can't see it in the short term. But, a significant downturn is quite possible. This question would need more analysis though