Ultimate bodhicitta refers to the wisdom realizing emptiness. Emptiness is regarded as the "ultimate" object, not because it is some sort of absolute truth that is independent of everything else. Rather, emptiness of inherent existence is the ultimate or deepest way in which all phenomena exist. Developing the wisdom realizing emptiness involves looking beyond superficial and deceptive conventional appearances.
In exploring the emptiness of inherent existence of phenomena, we are focusing on the ultimate truth, the deepest mode of existence of people and phenomena. The people and phenomena themselves are conventional truths, dependently existing things that appear with their own characteristics and perform various functions in the world. These two truths are related in that conventional truths are what appear to our mind on a day-to-day basis, while ultimate truths are their deeper mode of existence.
Nothing can ever be found that is self-existent or that exists by itself independently of other phenomena. Whatever appears to the mind, both inner objects related to sentient beings' minds and outer objects in the environment, is merely labeled by mind. If we analyze the final mode of existence of the subject – the mind which labels – we find it too is free from elaborations of the two extremes of true existence and total non-existence. Thus the final way of existing of both object and subject is that they do not exist from their own side. They are like space, which in this context is defined as a mere lack of tangibility and obstruction.
Wherever we look in space, we never find anything tangible or any impediment. Similarly, if we look for existence from its own side in any phenomenon, we never find it. We simply find freedom from the elaborations of the two extremes.