Fairness vs deservedness, allocation vs merit, these dichotomies might correspond well to the difference between flows and stocks.
To apportion who deserves which part of some past, fixed aggregation of value is likely more a matter of context than it is a matter of content, more about the general environment of the valuation than it is particular to the specific asset in question.
We need to take a step back and ask the question what does it mean to have a claim based on deserving something? Does it mean being able to consume the thing? Probably not. We typically don't have the right to waste an asset that was bequeathed to us. So the claim is a claim of stewardship rather than of private property.
To deserve is to have earned – but that which comes to us for having earned something is not the right to consume the thing but rather a corresponding enlargement of our person's 'asset' value. When we earn something, what we get is the projection of that value into our honor, dignity, distinguishedness, authority, and, ultimately, our power.
Power is the embodiment of earnedness because power is an asset as embodied in the person of the agent. Who owns what is a matter of who has power over it rather than which good becomes a part of whom's wealth, except insofar as wealth is power.