Manufacturing end-of-fiber optical components able to realize optical functions ranging from a simple lens to more complex functions such as mode selective components is a decisive but \emph{a priori} complex task owing to the fiber core dimensions. Effective low cost methods allowing to grow polymer components by free-radical photopolymerization using the light coming out of the fiber have recently been reported. A novel phenomenological model of the photopolymerization process underlying is here given and used to simulate the polymer component growth in a three dimensional time-resolved manner. The simulations results are thus used to understand and optimize the component growth conditions, focusing particularly on the role of oxygen either present in the atmosphere or dissolved in the solution.