Mining continues but the reward comes solely from transaction fees.

The algorithm makes it such that the last coin will be mined sometime around 2140. My assumption is that people just plan on moving to another fork before that point.

Miners are incentivised with transaction fees alone after all the bitcoins are mined.

> What happens when all the bitcoins are mined?

Then miners will get only the transaction fees. But it's still the same process. (Anyway, that won't happen, the number of available BTC to mining will asymptoptically approach 0, but will never get there.)