Based on observable data, I assume that there is a relationship
between the size, rigidity and the passage of time; that will result
in all objects subject to only their own gravitational influences
(Given: no body is ever truly uninfluenced by others) becoming
spherically shaped (round).
That's called hydrostatic equilibrium. That's one of the main factors that distinguish a dwarf planet from a smaller random piece of rock out there.
"A dwarf planet is an object the size of a planet (a planetary-mass object) but that is neither a planet nor a moon or other natural satellite. More explicitly, the International Astronomical Union (IAU) defines a dwarf planet as a celestial body in direct orbit of the Sun that is massive enough for its shape to be controlled by gravity, but that unlike a planet has not cleared its orbit of other objects."
There is no fixed size limit, because it depends on the composition.
"It had been thought that icy objects with a diameter larger than roughly 400 km are usually in hydrostatic equilibrium, whereas those smaller than that are not. Icy objects can achieve hydrostatic equilibrium at a smaller size than rocky objects. The smallest object that appears to have an equilibrium shape is the icy moon Mimas at 397 km, whereas the largest object known to have an obviously non-equilibrium shape is the rocky asteroid Pallas at 532 km (582×556×500±18 km). However, Mimas is not actually in hydrostatic equilibrium for its current rotation. The smallest body confirmed to be in hydrostatic equilibrium is the icy moon Rhea, at 1,528 km, whereas the largest body known to not be in hydrostatic equilibrium is the icy moon Iapetus, at 1,470 km."
So the range of transition between hydrostatic equilibrium and non-equilibrium is between approx 400 and 1500 km diameter and depends on a number of factors such as composition. There is no simple formula.
Dwarf planets are a good related topic, and I used them in the discussion, because many of them are above the limit of HE but close to it. But any cosmic body is subject to the same laws. Planets proper, moons, stars, etc - these all may be placed above or below the HE limit, depending mostly on size.
E.g. the Earth is clearly above the HE limit. But probably all comets are below it. A rock sitting in the dirt below your feet is clearly below it.