What is the minimum mass of a celestial object so that it can have a moon? I was wondering how massive something have to be so that it it can attract moons by pop culture standards (ellipsoid/round shape).
Could a planetoid have a moon? What is the relation between the mass of a moon and planet?
Planetoids can have moons and the minimum size is &quot;pretty small&quot;. For example 2003 SS84is a small Near-Earth asteroid, with a diameter of 120m and a moon of about 60m in diameter, which orbits at a distance of 270m ever 24 hours.  It probably didn't form by &quot;attracting the moon&quot; but the moon probably formed as a result of impact splitting a &quot;rubble pile&quot; asteroid.  The moon, in this case, is similar in size to the main object.  There is a wide distribution of size ratios from close to 1:1 to very small objects orbiting much larger ones.
However one aspect of your question is different:  you ask for a &quot;round&quot; shape. That makes things harder, since a round shape requires a fairly large size to pull the object into a sphere.  There is probably only one object except for the major planets, with a spherical moon, and that is Pluto with its moon Charon (and even Charon isn't perfectly rounded, but it is close)
So it is quite easy for a planetoid to have a moon.  But it is hard for a planetoid's to be big enough to pull itself into ellipsoidal equilibrium