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The propagation of low-Lewis-number premixed flames is analyzed in a partially confined Hele-Shaw chamber formed by two parallel plates separated a distance h apart. An asymptotic-numerical study can be performed for small gaps compared to the flame thickness deltaT . In this narrow-channel limit, the prob- lem formulation simplifies to a quasi-2D description in which the velocity field is controlled by domi- nant viscous effects. After accounting for conductive heat losses through the plates in our formulation, we found that the reaction front breaks into one or several isolated flame cells where the temperature is large enough to sustain the reaction, both in absence and in presence of buoyancy effects. Under these near-limit conditions, the isolated flame cells either travel steadily or undergo a slow random walk over the chamber in which the reacting front splits successively to form a tree-like pathway, burning only a small fraction of the fuel before reaching the end of the chamber. The production of quasi-2D circular or comet-like flames under specific favorable conditions is demonstrated in this paper, with convection, conductive heat losses and differential diffusion playing an essential role in the formation of the isolated one and two-headed flame cells.