Must two space bodies of same age have similar shape? Must two cosmic bodies (formed by gravitational forces) have similar shapes if they are located close to each other in the Universe and have the same age?
Thanx!
 A: It depends on how you define the "same" mass. 
Starting with the assumption that cosmic bodies cannot be formed during the Nucleosynthesis (the Big Bang excludes formation of elements heavier than the Lithium), you're left with a non-deterministic model. Nowadays, one popular theory to explain formation of cosmic bodies is the Chaotic Inflation (not the only one of course) and this is entirely based on the perturbative theory of a scalar field or in other words Quantum Mechanics. As you may know, Quantum Mechanics doesn't really like the word "same". The answer to your question is "Very unlikely" under that assumption. Chaotic inflation will give you a range of possible masses you could observe in the Universe though. 
Concerning the shape, depending on the mass, if you do not have the same infinitely precise initial conditions it becomes probabilistic. The only thing you can say is that Gravity is symmetric under rotations, meaning that the shape of the bodies should preserve such symmetries. A planet size body should always be a sphere...
I hope this can help you.
