  This paper provides a handy tool to compute the impact of Type Ia Supernova
(SNIa) on the evolution of stellar systems. An effective formalism is presented
to couple the SNIa rate to the star formation history, which rests upon the
definition of two key properties of the progenitor's model: the realization
probability of the SNIa event from a single stellar generation and the
distribution function of the delay times. It is shown that the current SNIa
rate in late type galaxies implies that the realization probability is on the
order of 0.001. Analytical formulations for the distribution function of the
delay times for Single (SD) and Double Degenerate (DD) progenitors are derived,
based on stellar evolution arguments. These formulations, which agree well with
the results of Monte Carlo simulations for the evolution of close binaries,
have a built in parametrization of the key properties of the alternative
candidates. The various models for the progenitors have different impact on the
large scales. In particular, the paper examines the systematic trend of the
SNIa rate per unit mass with the color of the parent galaxy, and shows that the
recent observations favor the DD model. The SD scenario can reproduce the data
only if the distribution of the primordial mass ratios is flat, and the
accretion efficiency onto the WD is close to 100%. The timescale for the Fe
release from SNIa to the interstellar medium ranges between 0.3 and 3 Gyr for a
wide variety of hypothesis on the SNIa progenitors. (ABRIDGED)
