At each step offer a fixed number of independent uniform candidate edges on a fixed vertex set, and let a rule select one. The standard two-choice model offers two candidates. The rule may depend on the entire previously exposed history. Repeated already present edges make no change in the independent-candidate version; another usual version offers only absent edges. The forced merging of large components and persistence of unsampled graph components apply to both over a linear number of steps. Fixed choice is essential in the continuity of fixed-choice percolation argument.
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