A melt blowing process comprising: (a) providing a thermoplastic polymer material that includes at least one or a plurality of polyester polymers and at least one or a combination of different meltable metal phosphinates; and (b) melt blowing the thermoplastic polymer material into at least one fiber or a plurality of fibers, with each fiber having a diameter or thickness that is less than about 10 microns. The metal phosphinate is in an amount that (a) reduces the viscosity of the polyester polymer and (b) functions as a crystallizing agent, which at least promotes crystallization of the polyester polymer, when the thermoplastic polymer material is melt blown into the at least one fiber. Non-woven and woven fibrous structures can be made using fibers made from this process.