Question about wiring up a distribution block

I'm trying to clean up my wiring. My plan is to run a single 1/0 gauge wire from my stereo battery on/off switch (which is hooked up to two Optima blue tops) to a distribution block, which will distribute the following:

a 4 gauge wire to an Alpine MRX-V70 (490 watts total output);
a 4 gauge wire to a Wetsounds HT1 (600 watts total output);
and an 8 gauge wire to an Alpine MRP-F300 (300 watts total output)

My question is whether the single 1/0 gauge wire is enough for the above. My guess is the answer is yes, but I want to make sure before I proceed. If not, I'll select a distribution block with more than one input and run additional wire to it.

P.S. David, if you read this, your mere suggestion that having my headunit on a switch and my amps off the switch was enough to cause me great angst. But I thank you nonetheless.

Yes, 1/0 will be plenty ample.

I didnt see any mention of over-current protection.
This, or something like it, placed at the source of power will cover all your needs. Do the math on wire size and length, not appliance load. This standard is in place to protect the wire, not the appliance.

Thanks for the responses guys. Bait, the distribution block I've selected is fused, but thanks for the heads up.