The spatial distribution of relatives has profound effects on kin interactions, inbreeding, and inclusive fitness. Yet, in the marine environment, the processes that generate patterns of kin structure remain understudied because larval dispersal on ocean currents was historically assumed to disrupt kin associations. Recent genetic evidence of co-occurring siblings challenges this assumption and raises the intriguing question of how siblings are found together after a (potentially) disruptive larval phase. Here, we develop individual-based models to explore how stochastic processes operating at the individual level affect expected kinship at equilibrium. Specifically, we predict how limited dispersal, sibling cohesion, and variability in reproductive success differentially affect patterns of kin structure. All three mechanisms increase mean kinship within populations, but their spatial effects are markedly different. We find that (1) when dispersal is limited, kinship declines monotonically as a function of the distance between individuals; (2) when siblings disperse cohesively, kinship increases within a site relative to between sites; and (3) when reproductive success varies, kinship increases equally at all distances. The differential effects of these processes therefore only become apparent when individuals are sampled at multiple spatial scales. Notably, our models suggest that aggregative larval behaviors, such as sibling cohesion, are not necessary to explain documented levels of relatedness within marine populations. Together, these findings establish a theoretical framework for disentangling the drivers of marine kin structure.