  We resolve spatially the star formation history of 300 nearby galaxies from
the CALIFA integral field survey to investigate: a) the radial structure and
gradients of the present stellar populations properties as a function of the
Hubble type; and b) the role that plays the galaxy stellar mass and stellar
mass surface density in governing the star formation history and metallicity
enrichment of spheroids and the disks of galaxies. We apply the fossil record
method based on spectral synthesis techniques to recover spatially and
temporally resolved maps of stellar population properties of spheroids and
spirals with galaxy mass from 10$^9$ to 7$\times$10$^{11}$ M$_{\odot}$. The
individual radial profiles of the stellar mass surface density ($\mu_{*}$),
stellar extinction (A$_{V}$), luminosity weighted ages ($\langle$ log age
$\rangle_{L}$), and mass weighted metallicity ($\langle$ log
Z/Z$_{\odot}$$\rangle_{M}$) are stacked in seven bins of galaxy morphology (E,
S0, Sa, Sb, Sbc, Sc and Sd). All these properties show negative gradients as a
sight of the inside-out growth of massive galaxies. However, the gradients
depend on the Hubble type in different ways. For the same galaxy mass, E and S0
galaxies show the largest inner gradients in $\mu_{*}$; and Andromeda-like
galaxies (Sb with log M$_{*}$(M$_{\odot}$) $\sim$ 11) show the largest inner
age and metallicity gradients. In average, spiral galaxies have a stellar
metallicity gradient $\sim$ -0.1 dex per half-light radius, in agreement with
the value estimated for the ionized gas oxygen abundance gradient by CALIFA. A
global (M$_{*}$-driven) and local ($\mu_{*}$- driven) stellar metallicity
relation are derived. We find that in disks, the stellar mass surface density
regulates the stellar metallicity; in spheroids, the galaxy stellar mass
dominates the physics of star formation and chemical enrichment.
