We have studied conformational properties of flexible polymers partially confined to narrow pores of different size using configurational biased Monte Carlo simulations under athermal conditions. The asphericity of the chain has been studied as a function of its center of mass position along the pore axis and as a function of the degree of penetration, or fraction of confined segments. The asphericity passes through a maximum well before all segments are located inside the pore. Rather than deforming gradually, we find that at intermediate penetration degrees, where the center of mass is within distances of approximately one radius of gyration away from the pore entry, the chain part inside the pore stretches out considerably while the remaining part outside the pore is coillike ("flower conformations"). When the center of mass is located further inside the pore, this strong chain extension along the pore axis diminishes, and the average conformation becomes that of a deformed coil. Introduction of weakly attractive monomer-wall interactions does not affect these observations significantly.