Pardon my noob question.
I have a question on mining operators. How do we know they are declaring 100% of the found blocks to the pool? Couldn't they simply skim a few blocks to an unknown entity once in a while?
Is this 100% based on trust?
A pool sends work in the form of a block header with a coinbase address to its miners. Solving this block pays the pool which in turn pays the miners according to that pool's payout algorithm. Miners also submit "shares" which are valid blocks with a lower difficulty than the current network value to the pool; the pool can determine how fast each miner is mining based on the frequency and difficulty of submitted shares. (Virtually every payout algorithm is based on valid submitted shares)
In order to solve a block that pays someone else, a mimer needs to mine a block with a coinbase address specifying where the block reward should go. This would mean solving a block different than the pool gave you, and would not count as a valid share on the pool, decreasing your hashrate on that pool. Therefore this is equivalent to splitting your hashrate between multiple pools. (Or partially solo mining)