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New mind fragments can control up to $0.0664\, \mathrm {m^3}$ of material (thats about human sized) and each century they can grow between 20% and 30% larger (volume). A new mind fragment starts anchored to a $0.1\, \mathrm{m^3}$ of suitable material at a temperature of 450°C. The alien mind requires a bare minimum of 1220 watts of energy, but 1500W is the recomended minimum. The energy requirements of the brain increase by an average of 20% every 50 years. New mind fragments can borrow energy from their 'parent' if needed. Assume that their methods of gathering energy from the sun/ambient heat are only 1% efficient. Each immortal alien needs enough room to gather energy for itself and to defend its energy gathering area. More power is better young immortals will need to defend their mineral deposites and collection areas from older immortals that want more energy and 'real estate'. For the sake of the question, energy is in demand.

Would the Sqare-Cube law prevent them from growing past a certain point? When would population become an issue? Which of energy absorbsion or living space become an issue first? How would their civilisation form itself? What other issues might they run into from being immortal and having these psychic powers?

New mind fragments can control up to $0.0664\, \mathrm {m^3}$ of material (thats about human sized) and each century they can grow between 20% and 30% larger (volume). A new mind fragment starts anchored to a $0.1\, \mathrm{m^3}$ of suitable material at a temperature of 450°C. The alien mind requires a bare minimum of 1220 watts of energy, but 1500W is the recomended minimum. The energy requirements of the brain increase by an average of 20% every 50 years. New mind fragments can borrow energy from their 'parent' if needed. Assume that their methods of gathering energy from the sun/ambient heat are only 1% (see Edit below) efficient. Each immortal alien needs enough room to gather energy for itself and to defend its energy gathering area. More power is better young immortals will need to defend their mineral deposites and collection areas from older immortals that want more energy and 'real estate'. For the sake of the question, energy is in demand.

Would the Sqare-Cube law prevent them from growing past a certain point? When would population become an issue? Which of energy absorbsion or living space become an issue first? How would their civilisation form itself? What other issues might they run into from being immortal and having these psychic powers?

Edit: As per my coment on Murphy's answer, newborns have a heat-to-energy efficiency of 20%-30% which stays constant for the first century but then drops to 1% after about a miilennia. This (correctly and awesomely) means that "the oldest, largest and post powerful would also be the most greedy".

New mind fragments can control up to 0.0664 m^3 of material (thats about human sized) and each century they can grow between 20% and 30% larger (volume). A new mind fragment starts anchored to a 0.1 m^3 of suitable material at a temperature of 450°C. The alien mind requires a bare minimum of 1220 Watts of energy, but 1500w is the recomended minimum. The energy requirements of the brain increase by an average of 20% every 50 years. New mind fragments can borrow energy from their 'parent' if needed. Assume that their methods of gathering energy from the sun/ambient heat are only 1% efficient. Each immortal alien needs enough room to gather energy for itself and to defend its energy gathering area. More power is better young immortals will need to defend their mineral deposites and collection areas from older immortals that want more energy and 'real estate'. For the sake of the question, energy is in demand.

New mind fragments can control up to $0.0664\, \mathrm {m^3}$ of material (thats about human sized) and each century they can grow between 20% and 30% larger (volume). A new mind fragment starts anchored to a $0.1\, \mathrm{m^3}$ of suitable material at a temperature of 450°C. The alien mind requires a bare minimum of 1220 watts of energy, but 1500W is the recomended minimum. The energy requirements of the brain increase by an average of 20% every 50 years. New mind fragments can borrow energy from their 'parent' if needed. Assume that their methods of gathering energy from the sun/ambient heat are only 1% efficient. Each immortal alien needs enough room to gather energy for itself and to defend its energy gathering area. More power is better young immortals will need to defend their mineral deposites and collection areas from older immortals that want more energy and 'real estate'. For the sake of the question, energy is in demand.

I am writing a story with an immortal race of aliens with psychic powers. Their minds are separate from their bodies and located in a pocket dimension inaccessible to ordinary matter. Their bodies are psychicly animated stone or metal. (Like Astral projection?)

• They can die temporarily (ie: get disconnected from their body) by being crushed or vapourised. They can re-animate their original body or construct a new body from material in a 100m radius of where they died. They can also die permanently if they run out of energy and have no way of getting more.

• They can only control one body at a time. Only one immortal can control one body at a time.

• Older immortals are more powerful than young ones. Old immortals generally control larger bodies and have more powerful psychic powers. Immortals are motivated to have large bodies because this gives them increased awareness of the world around them. They can only communicate and interact with each other through the physical world, mind-to-mind communication is impossible. Their bodies act as an 'anchor' and allow them to interact with the physical world so the loss of a body entails complete loss of contact with everyone.

• They reproduce slowly (compared to humans) with a new generation every 250-500 Earth years. Reproduction is like mitosis, the mind splits a little bit off. This mind fragment will have to construct a new body for itself.

• Cancer or other diseases are not an issue but they need to absorb energy or they will become less powerful and later completely impotent. Energy can be absorbed as Heat. They take advantage of the energy gradient between their home dimension and their body in order to absorb energy. Using their psychic powers drains energy and they can absorbe energy through their stone/metal bodies. Larger bodies require more energy (proportional to the weight that needs to be moved) but can also absorb more energy (absorbsion is proportional to the surface area of the body).

• The immortal aliens prefer hot rocky planets, like Venus and Io (Jupiter's Moon) and are currently about Kardashev I or a little below. They can only use solid rocks or metal for their bodies and have access to most surface minerals. They are not a highly technological species, they prefer to use their psychic powers. They only need energy (solar prefered) and a suitable material for their bodies. Material for shelter is optional. They can only anchor to solid objects.

• Their psychic powers include Telekinesis, Levitaion and Pyrokinesis. Moving an object telekinetically requires the same amount of energy as moving it by normal means. The same with Levitation and Pyrokinesis. Using the body to move objects is more energy efficient than using telekinesis. Since their body acts as an 'anchor' for the mind, destruction of the body means a loss of access to psychic powers. Creating a psychic effect further from the body uses more energy, proportional to distance. (Probably the square of distance).

I am writing a story with an immortal race of aliens with psychic powers. Their minds are separate from their bodies and located in a pocket dimension inaccessible to ordinary matter. Their bodies are psychicly animated stone or metal.

• They can die temporarily (ie: get disconnected from their body) by being crushed or vapourised. They can re-animate their original body or construct a new body from material in a 100m radius of where they died. They can also die permanently if they run out of energy and have no way of getting more.

• They can only control one body at a time. Only one immortal can control one body at a time. Control over their bodies relies on the (cross sectional) area of each limb, stick-like limbs are not as strong as tree trunk-like limbs.

• Older immortals are more powerful than young ones. Old immortals generally control larger bodies and have more powerful psychic powers. Immortals are motivated to have large bodies because this gives them increased awareness of the world around them. They can only communicate and interact with each other through the physical world, mind-to-mind communication is impossible. Their bodies act as an 'anchor' and allow them to interact with the physical world so the loss of a body entails complete loss of contact with everyone.

• They reproduce slowly (compared to humans) with a new generation every 250-500 Earth years. Reproduction is like mitosis, the mind splits a little bit off. This mind fragment will have to construct a new body for itself.

• Cancer or other diseases are not an issue but they need to absorb energy or they will become less powerful and later completely impotent. Energy can be absorbed as Heat. They take advantage of the energy gradient between their home dimension and their body in order to absorb energy. Using their psychic powers drains energy and they can absorbe energy through their stone/metal bodies. Larger bodies require more energy (proportional to the weight that needs to be moved) but can also absorb more energy (absorbsion is proportional to the surface area of the body).

• The immortal aliens prefer hot rocky planets, like Venus and Io (Jupiter's Moon) and are currently about Kardashev I or a little below. They can only use solid rocks or metal for their bodies and have access to most surface minerals. They are not a highly technological species, they prefer to use their psychic powers. They only need energy (solar prefered) and a suitable material for their bodies. Material for shelter is optional. They can only anchor to solid objects.

• Their psychic powers include Telekinesis, Levitaion and Pyrokinesis. Moving an object telekinetically requires the same amount of energy as moving it by normal means. The same with Levitation and Pyrokinesis. Using the body to move objects is more energy efficient than using telekinesis. Since their body acts as an 'anchor' for the mind, destruction of the body means a loss of access to psychic powers. Creating a psychic effect further from the body uses more energy, proportional to distance. (Probably the square of distance).