It would only be extended with new transactions, not blocks. Computational resources will be devoted to verification rather than brute-forcing hashes (a much less computationally intensive matter).
No, blocks are still created in exactly the same way, the only difference is that no new bitcoins are created as a side-effect. It is necessary for new transactions to be locked into the block chain with a bruteforced hash, as it's this expenditure of processing power that makes the transactions permanent and prevents double-spending.
I just imagined that the bitcoin world post-mining (after or near the 21M BTC is reached) would just consist of the transactional interfaces and not need the specialized GPU miners.
Unfortunately, that's not how it works. The "miners" are really "transaction settlers". It's the longest block chain that represents the globally consistent view of which transactions have settled.
OK, that was an aspect I was unfamiliar with. So after the mining phase ends, transactions become zero-sum BTC games, where the biggest 'miners' accrue their proportional share of the total fees of transactions validated.
