This article examines how kinship forms a contested element of labour under capitalist distribution. The focus of the article is on a thriving Spanish container port where the dockworker collective has been steadily growing since the multinational companies first arrived in the 1970s. In the wake of containerization – a standardized system of freight transport based on the intermodal shipping container – dock work has been revalued and become attractive in an area otherwise characterized by high unemployment rates and below-average salaries. Drawing on ethnographic research, the article analyses how unionized dockworkers are met with stigmatization from the general public and criticized for their intergenerational access to ‘container capital’. The article contributes to current anthropological debates around the role of labour under global capitalism by tracing the links between kinship and labour in the making of a global port.