  In a recent survey of the stellar populations of LINERS and LINER/HII
Transition Objects (TOs) we identified a numerous class of nuclei which stand
out because of their conspicuous 10^8-9 yr populations. These objects were
called ``Young-TOs'', since they all have TO-like emission line ratios. In this
paper we investigate the radial variations of spectral properties in Low
Luminosity AGN. Our analysis is based on high S/N, 3500-5500 A, long-slit
spectra for 47 galaxies. The data probe distances of typically up to 850 pc
from the nucleus with a resolution of ~ 100 pc and S/N ~ 30. Stellar population
gradients are mapped by the radial profiles of absorption line equivalent
widths and colours along the slit. These variations are further analyzed by
means of a decomposition of each spectrum in terms of template galaxies
representative of very young (<= 10^7 yr), intermediate age (10^8-9 yr) and old
(10^10 yr) populations.
  Our main findings are: (1) Significant stellar population gradients are found
almost exclusively in Young-TOs. (2) The intermediate age population of
Young-TOs, although heavily concentrated in the nucleus, reaches distances of
up to a few hundred pc. (3) Objects with predominantly old populations present
spatially homogeneous spectra, be they LINERs or TOs. (4) Young-TOs have much
more dust in their central regions than other LLAGN. (5) The B-band
luminosities of the central <~ 1 Gyr population in Young-TOs are within an
order of magnitude of M_B = -15, implying masses of order ~ 10^7-10^8 Mo. This
population was 10-100 times more luminous in its formation epoch, at which time
young massive stars would have completely outshone any active nucleus, unless
the AGN too was brighter in the past. (abridged)
