I always assumed that emini contracts were being offset by positions in the regular S&P. In other words, a 'big' trader would buy the S&P and offset it by sellng ES to smaller traders. Don't know why I thought this. Coincidental maybe: 32,000 S&P contracts is equal to 1.6 million ES contracts.
If you are trading this size and using Interactive Brokers you would be wise to familiarize yourself with Zeroling Trader or Button Trader (info can be found at the IB website). Good Luck.