We introduce a new self-consistent structure finding algorithm that parses large scale cosmological structure into clusters, filaments and voids. This algorithm probes the structure at multiple scales and classifies the appropriate regions with the most probable structure type and size. We use this structure finding algorithm to parse and follow the evolution of poor clusters, filaments and voids in large scale simulations. We trace the complete evolution of the baryons in the gas phase and the star formation history within each structure. We vary the structure measure threshold to probe the complex inner structure of star forming regions in poor clusters, filaments and voids.  We find the majority of star formation occurs in cold condensed gas in filaments at all redshifts and that it peaks at intermediate redshifts (z ~ 3). We also show that much of the star formation above a redshift z = 3 occurs in low contrast regions of filaments, but as the density contrast increases at lower redshift, star formation switches to high contrast regions or the inner parts of filaments.  Since filaments bridge between void and cluster regions, this suggests that the majority of star formation occurs in galaxies in intermediate density regions prior to the accretion onto poor clusters. We find that at the present epoch, the gas phase distribution is 43.1%, 30.0%, 24.7% and 2.2% in the diffuse, WHIM, hot halo and condensed phases, respectively. Most of the WHIM is found to be in filamentary structures. Moreover 8.77%, 79.1%, 2.11% and 9.98% of the gas is located in poor clusters, filaments, voids and unassigned regions respectively. We find that both filaments and poor clusters are multiphase environments at redshift z = 0.