Proof that Delta and Y transformer have the same power?
Which means I have 3 times the power in the Delta configuration vs
  what I had with star configuration


Yup, that's what happens. In Y formation, one primary receives \$\frac{1}{\sqrt3}\$ of the line voltage and, for a given resistive load output, there is \$\frac{1}{\sqrt3}\$ of load current. Because V x I = power, the power is only \$\frac{1}{3}\$ of what it is when connected in delta.

Application: a star/delta configuration is used to start induction motors. You begin in start (one third the power) and when it's close to full speed you switch the windings to delta.