What determines the amp rating of a transformer? Many aren't marked. Is it simply the wire size of one side or the other?

I notice that some transformers have thin wire on one side and thick wire on the other one. Why thick and thin? Thin seems to have the benefit of more wraps, but seems that it would have a lower amp rating and more resistance. The thick wire seems to be limited to fewer wraps, seems that it would have more amp capacity and it obviously has lower resistance.

Is there a chart where I can determine the amp rating of a transformer based on wire size alone?

[This message has been edited by Spark Master Flash (edited 12-21-2005).]