Redistribution of Charge between Conductors

Two conductors joined by a wire form one conductor, so they come to one potential. For two distant spheres $V_1 = V_2$ gives $Q_1/R_1 = Q_2/R_2$, so the charge splits in proportion to radius and the common potential is $kQ/(R_1 + R_2)$. Because $E = V/R$ at each surface, the smaller sphere ends with the stronger field and the higher surface density even though it holds less charge. Grounding is the same condition with earth as the partner: it fixes $V = 0$ and lets whatever charge that demands flow in or out.

Two errors dominate. Splitting the charge evenly between unequal conductors, or equalizing surface charge density instead of potential, both of which leave the system with a potential difference across a conducting wire. And treating a ground wire as a drain that always empties a conductor: it empties an isolated sphere with nothing nearby, but next to a fixed positive charge it delivers negative charge instead, which is exactly how charging by induction works.