That's a somewhat difficult question to answer. I guess you could say that so long as the Masterghost "their soul" exists, they can fight. If the "Master" is K.O.'d the Masterghost takes a huge hit in HP, but its barrier will still remain. No matter how many times the Master is defeated, the Masterghost will still function, so in a way it is their spiritual base, however
Capture Units can easily capture other Ghosts "or spiritual bases" as an extension of the Masterghost's power, this in turn can restore the Master's HP, Tension, and the HP of his Servants. However, Capture Units are incredibly weak by comparison. So in a way they act as a "heartbeat". So long as another Masterghost and Master exists, they cannot capture the entire field, even if the Masters do nothing, as the Capture Units will basically destroy eachother on contact. This is somewhat like how the "ego" works, as long as there is a field of influence (or a desire to win/fight at least), the capture Units would keep pumping themselves out of the Master Ghost.
Lastly you have the Master and Servants and Mobile Minion. The Master serves as the central "active" extension of the Masterghost, meanwhile his Servants are to some extent representatives of his personality in various capacities based on need and adaptivity. But because they are more active than Capture Units, they require Mana to be summoned, Mana is generated by destroying other units and capturing Ghosts. This is also why destroying a Servant won't hurt the Masterghost or Master directly. Lastly, you have Mobile Minions, they are similar in Function to a Servant, but require Tension, not Mana to summon.
One other thing, only Servants and Mobile Minions can destroy a Masterghost's barrier, but they cannot actually "kill" the Masterghost, since they are Mana and Tension manifestations, the Master himself has to land the killing blow. A Master can wail on a Masterghost's barrier for a long period of time and do chip damage, but only Tension Attacks would actually do damage.
Something else worth noting:
Sol: Uses Soul Sinker System
Valentine: Uses Soul Sinker + Vizuel (Vizuel are a type of Youkai existence generated from Valentine's 'intent' created in the Backyard)
Izuna: Has his Youkai friends help him.
Paradigm: Has his Gear friends help him.
Sin + Ky: Uses soldiers of Illuriya Kingdom's Army. Sin can still summon a Mobile Minion, however.
Raven: Uses Soul Sinker via Valentine's servants.
I'm not entirely sure if Soul Sinker has anything to do with Gear Sublimation, but it may seem that way, as Sin and Sol were unable to move at first, and would have been sublimated if Izuna had not intervened.