The morphology of amorphous solid water grown by vapor deposition was found to depend strongly on the angular distribution of the water molecules incident from the gas phase. Systematic variation of the incident angle during deposition using a collimated beam of water led to the growth of nonporous to highly porous amorphous solid water. The physical and chemical properties of amorphous solid water are of interest because of its presence in astrophysical environments. The ability to control its properties in the laboratory may shed light on some of the outstanding conflicts related to this important material.