power - Voltage sources in parallel?

I've looked at other questions "Voltage sources in parallel", but don't answer my specific problem.

Imagine the following circuit:

^{simulate this circuit – Schematic created using CircuitLab}

I have a solar powered charge controller that, ideally, can deliver 30A at 14.0V, and a battery that, ideally, can deliver unlimited current at 12.8V.

Which laws can tell me something about how this circuit will behave?

For example, if the load is a 50W LED, it would need 14V at 3.57A. Would all the current and voltage come from the CC, because it has a higher voltage?

When the total current would be higher than 30A, I suspect the CC would fail to sustain the voltage.

Answer

"Would all the current and voltage come from the CC, because it has a higher voltage?"

Exactly.

The higher voltage from the CC biases the battery's diode so it will not conduct.

(Also, the diodes will reduce the voltage by about .7 volts.)