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Abstract We study a general flat space/boson star transition model in quasi-local ensemble through approaches familiar from holographic superconductor theories. We manage to find a parameter ψ 2, which is proved to be useful in disclosing properties of phase transitions. In this work, we explore effects of the scalar mass, scalar charge and Stückelberg mechanism on the critical phase transition points and the order of transitions mainly from behaviors of the parameter ψ 2. We mention that properties of transitions in quasi-local gravity are strikingly similar to those in holographic superconductor models. We also obtain an analytical relation ψ 2 ∝ (μ − μ c )1/2, which also holds for the condensed scalar operator in the holographic insulator/superconductor system in accordance with mean field theories.