Odorant transport is of fundamental and applied importance. Using computational simulations, we studied odorant transport in an anatomically accurate model of the nasal passage of a hagfish (probably Eptatretus stoutii). We found that ambient water is sampled widely, with a significant ventral element. Additionally, there is a bilateral element to olfactory flow, which enters the single nostril in two narrow, laminar streams that are then split prior to the nasal chamber by the anterior edge of the central olfactory lamella. An appendage on this lamella directs a small portion (10–14%) of the overall nasal flow to the olfactory sensory channels. Much of the remaining flow is diverted away from the sensory channels by two peripheral channels. The anterior edge of the central olfactory lamella, together with a jet-impingement mechanism, disperses flow over the olfactory surfaces. Diffusion of odorant from bulk water to the olfactory surfaces is facilitated by the large surface area:volume ratio of the sensory channels, and by a resistance-based hydrodynamic mechanism that leads to long residence times (up to 4.5 s) in the sensory channels. With increasing volumetric flow rate, the rate of odorant transfer to the olfactory surfaces increases, but the efficiency of odorant uptake decreases, falling in the range 2–6%. Odorant flux decreases caudally across the olfactory surfaces, suggesting in vivo a preponderance of olfactory sensory neurons on the anterior part of each olfactory surface. We conclude that the hagfish has a sophisticated anatomy for locating and capturing odorant molecules.