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This paper examines childbearing among Polish migrant women and their descendants in Sweden. Unlike most studies on migrant fertility, we do not rely solely on a comparison between different migrant generations and the natives in the country of destination. Instead, we also consider the non-migrants in the country of origin. This unconventional country-of-origin and country-of-destination approach is preferable to more carefully examine the relevance of three migrant fertility hypotheses, namely the socialization, the selection and the adaptation hypotheses. Based on a piecewise-exponential model, the transitions to first and second births are analyzed using Swedish register data and the Polish Generations and Gender Survey (GGS). The results show that the Polish stayers and the first-generation Polish immigrants are similar in terms of the timing of births but are more different in terms of quantum. Selection into migration and compositional differences can, to some extent, explain both similarities and differences between the first-generation migrants and the Polish stayers and Swedish natives. For example, when introducing cohort in the second-birth analysis, the socialization hypothesis is confirmed for the younger cohorts. Examining the second-generation in relation to the Swedish natives, we find convergence of fertility behavior across migrant generations both in terms of quantum and timing.