Following Paper I we investigate the properties of atmospheres that form around small protoplanets embedded in a protoplanetary
disc by conducting hydrodynamical simulations. These are now extended to three dimensions, employing a spherical grid centred
on the planet. Compression of gas is shown to reduce rotational motions. Contrasting the 2D case, no clear boundary demarcates
bound atmospheric gas from disc material; instead, we find an open system where gas enters the Bondi sphere at high latitudes
and leaves through the mid-plane regions, or, vice versa, when the disc gas rotates sub-Keplerian. The simulations do not
converge to a time-independent solution; instead, the atmosphere is characterized by a time-varying velocity field. Of particular
interest is the time-scale to replenish the atmosphere by nebular gas, treplenish. It is shown that the replenishment rate,
Matm/treplenish, can be understood in terms of a modified Bondi accretion rate, ∼R2BondiρgasvBondi, where vBondi is set by
the Keplerian shear or the magnitude of the sub-Keplerian motion of the gas, whichever is larger. In the inner disc, the atmosphere
of embedded protoplanets replenishes on a time-scale that is shorter than the Kelvin-Helmholtz contraction (or cooling) time-scale.
As a result, atmospheric gas can no longer contract and the growth of these atmospheres terminates. Future work must confirm
whether these findings continue to apply when the (thermodynamical) idealizations employed in this study are relaxed. But
if shown to be broadly applicable, replenishment of atmospheric gas provides a natural explanation for the preponderance of
gas-rich but rock-dominant planets like super-Earths and mini-Neptunes.