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Conical transitions have wide applications in wind turbine foundation as well as oil and gas jacket type of structures. The junctions where tubular and cone meet experience a sharp stress rise from shell edge effects. Like all structures experiencing sharp stress rises, fatigue considerations are critical. In addition to fatigue, the existing offshore structural design standards also require ultimate limit state checks. It is known from the lower bound theorem of plasticity limit analysis that the junction local edge effects do not impact the global capacity. Designing for the local junction ultimate limit state contains wide variations among existing design standards. In this paper, the design practices from API RP-2A, NORSOK N-004, and ISO 19902:2020 draft are assessed. They are compared to the shell plastic yield criteria of Hodge and Ilyushin. In addition, this paper provides a semi-analytical plasticity solution to determine junction plastic deformations. The formulation is based on cylindrical shell equations coupled with deformation plasticity theory. It is found that the growth of the junction plasticity zone is limited, which is consistent with the anticipation from the lower bound limit analysis theorem. The observations made in this paper show that the local junction plasticity is a secondary issue compared to other design considerations. Its ultimate limit state design equation can afford to be more lenient if chooses for future standards' development. [ABSTRACT FROM AUTHOR]