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Economic inequality develops on multiple dimensions, such as the wealth disparities within countries and between countries. While immigration is often considered an individual strategy to escape structural disadvantage, its simultaneous influence on domestic within-country and global between-country inequality is rarely examined. This study advances the discussion through agent-based models that simulate different immigration types, remittance flows, and different economic conditions across countries that interact to shape inequality dynamics. Using weighted and unweighted Theil indices, we test the effect of immigration on within- and between-country inequality concurrently. The simulation results reveal the nonlinear relation of immigration and inequality, shaped by different immigration types and the economic growth rates across countries in the growing globalized inequality context.