Yeah, I had the starbase idea too, but the AI quickly countered by simply staying away from them. Most irritating.

In terms of splitting the fleets, what would you recommend in the smaller sub-groups?

First, get some fighters (use carriers, upgrade your starbase, build hangers, whatever is most convenient).  Set the fighters to "hold ground" stance and position them around the starbase.  Build a few flak frigates and do the same.  This should render the starbase impervious to most forces of strike craft.  Now upgrade the starbase with "auxiliary government".  This means control of the planet cannot be lost even if it's reduced to 0 HP through bombardment.  This forces the enemy to attack the starbase if they want the planet.

A Sova Carrier with a few gardas, hoshikos, and javelis is a superb force.  The Sova can field bombers or fighters and if it reaches level 6 you can use its ultimate ability to quickly swap between fighters and bombers on the fly depending on what enemy unit types you're facing.  Combined with its combat abilities, the Sova can counter virtually any combat units, and the simple forces of gardas, hoshikos, and javelis makes a balanced escourt.  If you're facing primarily heavy cruisers, then go with light carriers equipped with bombers.  Either hide under the protection of a starbase or else linger on the edge of the gravity well so you can jump out if the enemy gets too close.

Sure you can.  It just means you need to put some frigates on support duty.  Use hoshikos instead of repair platforms, a few carriers for strike craft, and maybe supplement its firepower with a few Javelis LRM's.  If you really want to play hard-ball, station an Akkan battlecruiser next to the starbase with targeting uplink.  Asteroid belts give all units a chance to miss, but targeting uplink will negate most of that, plus it will grant your units an attack range bonus (always nice).  You should be able to hold an asteroid belt against all but the most dedicated attacks.

If you're doing a lot of fighting in asteroid belts, bring in the Akkan and use targeting uplink.  If you can level it up, armistice is a real game-winner.  One of my favourite armistice antics is to rig a starbase to explode.  I then maneuver my Akkan so that when I activate armistice (hoover your cursor over the icon for a preview of its radius) only my own fleet is affected, and the starbase and enemy fleet are not.  I think activate armistice, then blow the starbase.  Armistice technically makes the affected units invulnerable, so they survive the blast unharmed while the enemy fleet is torched. 

If the AI is focusing mainly on heavy cruisers, capital ships, and carriers, you might want to focus on mostly carriers with bombers, plus flak. As long as you make sure your bombers don't run into Phasic Trap, taking down the AI's fleet shouldn't be that difficult. It'd be easiest if you can get to fight the AI in a neutral or friendly gravity well, where your carriers can just perch on the edge and bomb the enemy's HCs and caps with inpunity. The AI just doesn't know what to do if there are more than 50ish bomber squadrons decimating its fleet.

Found where it was hiding its response fleets. If the AI does this to you then check some of the asteroid fields, this is where my AI was hiding his ships. Easy to win now, sent my main fleet to lock down his supply depot and set my raiders loose on his worlds; sub fleet idea works really well here.

Darvin3 has the best solution to your problem. But I would also add that that asteroid belt is a cap leveling bonanza!!!

Have a starbase there with full weapon upgrades and Max resupply. Rest distribute between armor and strike craft to your liking. That resupply skill combine with hoshikos is gonna be insane since your can just let your hoshikos go spam crazy on booth repair-bots and demo-bots and they won't run out of AM. About 20 would be super. LRFs definitely, place them on hold position around the starbase hugging it with the Akkan. Having a Marza there will also help a great deal once it reaches lvl6. 10 light carriers with the SC of your choice depending on what the AI is bringing, have the SC on local area engagement only. And add a few flaks if he is SC heavy. If your used this setup right you can use the little asteroid belt to milk XP from him to level up all of your caps to lvl10 rather quickly if you do it right by rotating in a 3rd cap ship in constantly.

But your taking 20% lest damage. You with an Akkan with lvl3 targeting uplink you only lose 55 DPS. For TEC in an astroid belt with and Akkan you can do wonders!!! The targeting uplink skill goes from being mostly sucky to being almost godly.

Im cheering for vasari.