  Giant planets are thought to have cores in their deep interiors, and the
division into a heavy-element core and hydrogen-helium envelope is applied in
both formation and structure models. We show that the primordial internal
structure depends on the planetary growth rate, in particular, the ratio of
heavy elements accretion to gas accretion. For a wide range of likely
conditions, this ratio is in one-to-one correspondence with the resulting
post-accretion profile of heavy elements within the planet. This flux ratio
depends sensitively on the assumed solid surface density in the surrounding
nebula. We suggest that giant planets' cores might not be distinct from the
envelope and includes some hydrogen and helium, and the deep interior can have
a gradual heavy-element structure. Accordingly, Jupiter's core may not be
well-defined. Accurate measurements of Jupiter's gravitational field by Juno
could put constraints on Jupiter's core mass. However, as we suggest here, the
definition of Jupiter's core is complex, and the core's physical properties
(mass, density) depend on the actual definition of the core and on its growth
history.
