  We use a variational approach to gain insight into the strongly correlated
d-wave superconducting state of the high Tc cuprates at T=0. We show that
strong correlations lead to qualitatively different trends in pairing and phase
coherence: the pairing scale decreases monotonically with hole doping while the
SC order parameter shows a non-monotonic dome. We obtain detailed results for
the doping-dependence of a large number of experimentally observable
quantities, including the chemical potential, coherence length, momentum
distribution, nodal quasiparticle weight and dispersion, incoherent features in
photoemission spectra, optical spectral weight and superfluid density. Most of
our results are in remarkable quantitative agreement with existing data and
some of our predictions, first reported in Phys. Rev. Lett. {\bf 87}, 217002
(2001), have been recently verified.
