Star formation cannot proceed without the existence of an extensive gas reservoir. In particular, the supply of gas to form stars in dwarf galaxies and star clusters requires overcoming a variety of difficulties - namely, the effectiveness of different feedback mechanisms in removing gas from these shallow gravitational potentials. In addition, the supply of external gas to these systems is determined by the large scale galactic structure in which they reside. This thesis employs computational hydrodynamics coupled with physically realistic subgrid feedback prescriptions to resolve the interplay between the small scale feedback mechanisms and larger scale gas flows to determine the amount of gas a shallow potential can accumulate.

First, we consider the flow of gas external to dwarf galaxies and star clusters into their cores as a generalized accretion process. Second, we explore the enhancement of gas accretion rates onto the compact members of young star clusters when the flow of external gas into the cluster cores is large. Third, we discuss how external gas flows initiated by the presence of a massive nuclear star cluster can enhance central massive black hole accretion rates during galaxy mergers. Fourth, we change our focus to exploring internal stellar wind retention in proto-globular clusters as a mechanism to supply gas for multiple episodes of star formation. Finally, the implications of stellar wind retention on the current gas reservoir in globular clusters is discussed.