  We study the structure of generalized parton distributions in spin 0 nuclei
within a microscopic approach for nuclear dynamics. GPDs can be used on one
side as tools to unravel the deep inelastic transverse structure of nuclei in
terms of both transverse spatial and transverse momentum degrees of freedom. On
the other, one can obtain information on GPDs themselves by observing how they
become modified in the nuclear environment. We derive the structure of the
nuclear deeply virtual Compton scattering tensor and generalized parton
distributions at leading order in $Q$ in a field-theoretical framework. The
nuclear generalized parton distributions are calculated using a two step
process -- the convolution approach -- where the scattering process happens
from a quark inside a nucleon, itself inside a nucleus, disregarding final
state interactions with both the nuclear and nucleon debris. We point out that
details of the nuclear long range interactions such as two-body currents, can
be disregarded compared to the deep inelastic induced modifications of the
bound GPDs. We show how the pattern of nuclear modifications predicted, and in
particular the deviations of off-shell effects from the longitudinal
convolution provide clear signals to be sought in experimental measurements.
Finally, we find interesting relationships by studying Mellin moments in
nuclei: in particular we predict the $A$-dependence for the $D$-term of GPDs
within a microscopic approach, and the behavior with $t$ of the total momentum
carried by quarks in a nucleus. The latter provides an important element for
the evaluation of nuclear hadronization phenomena which are vital for
interpreting current and future data at RHIC, HERMES and Jefferson Lab.
