According to the popular Solar System formation models, what are the bounds on the Gas Giants' cores (note I am only interested in the bounds for our Solar System).
For example according to Wikipedia on Jupiter
Assuming [a core] did exist, it may have shrunk as convection currents of hot liquid metallic hydrogen mixed with the molten core and carried its contents to higher levels in the planetary interior.
This suggests that a core would shrink over time, which would put an upper bound on the size today.
Are there other bounds? I would like numbers together with some reasons for those numbers.