I'm going to make a different suggestion than the others who've replied so far and hope i don't step on any toes.
I agree with the relay for remote, i did that when i got up to 4 amps, you don't want to draw to much current from your HU. And i also used to have separate power cables for each amp from the battery.
But, when you get up to that much power, I think you need a 1 f cap.
I was running close to 1000w rms and lights would dim at high volume and bass would sound muddy. I added the cap, only on the amps for the subs, and it made a big difference. The problem isn't not enough current, but not enough current fast enough! I was really impressed with how much difference the cap made. Since i wasn't pulling down the voltage with the sub amps, even the amps for mid & highs sounded better.
Then i got carried away and bought more speakers and more amps. Then i had to break down and run a fused 1/0 cable and distribution blocks. And of course a new 2f cap. You can really get carried away with all this stuff...
I just ripped the whole system out of my old car and it's sitting in my bedroom waiting to be installed in my new car. I'm suffering audio withdrawls, waiting for new subs to be delivered.