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If I use the oject TMySqlXXConnection to create a commercial application, I pay for the license to mysql?
Starting from MySQL 5.0, yes. MySQL splits its development into community and enterprise edition, the former may only be used if you're creating open source apps.
Why in the latter case it should be possible not to pay!
Which case? Used sockets? If yes, then the answer would be because sockets are implemented in OS libraries and it's allowed (to the best of my knowledge, no OS forces you to pay because you're using its socket API) to be used in commercial apps.