Maximum voltage and current input of this circuit?
Look at the data sheet for the 2N3055 and note that the maximum power dissipation is ~115 W with an excellent heat sink, and that the maximum current rating is 15 A. 12 VDC at 15 A could theoretically produce 180 W out, but that would be for a "perfect" switching device with no dissipation. This circuit does not use the most efficient switching mode, so considerable power is wasted in heating the transistor.

That said, the circuit you show, apparently from Instructables, should work, actually producing a few thousand volts at a milliamp or two... far less than your suggested 600 W. This is a good thing, as one could get serious RF burns from a 600 W RF supply.

To get higher voltage, bypass the resistors with capacitors, as shown at PocketMagic. To get yet more voltage, the primary of the flyback transformer should resonate with the secondary, using an experimentally-determined capacitor. 

If you make it, use a larger heat sink than that shown -- perhaps a heavy aluminum fry pan, with bottom filed flat. Use thermal compound, as well. In any case, the transistor will likely fail, particularly if you use more than 12 VDC. If it doesn't fry from overheating, high-voltage transients on the primary will likely destroy it. Still, this is a simple circuit, provides a learning opportunity, and is fun as long as it lasts.

More power can be output by this two-transistor push-pull circuit from RimStar, or the more complex one at Silicon Junction. The LM555 circuit could easily be made with frequency variable to determine if tuning affects spark length and current. BTW, a rough estimate of output voltage: between rounded conductors, ~1 kV/mm for the intial spark length.