The stigma has a surface that chemically bonds to the specific coating on the pollen from its own species, so it captures its own pollen very well but not the pollen of other species of plant. Stigma surfaces can be either wet or dry.
Different plants have widely different varieties of pollen coatings, stigma surfaces, slime layers and other structures made to specifically bind the pollen and stigma of the same species together, according to a study by Edlund, Swanson and Preuss. After the initial adhesion of the pollen to the stigma, various processes often work to make the bond stronger. The pollen is generally very dry when it first comes in contact with the stigma, so once they are firmly bonded, the stigma begins providing water to the pollen to allow it to grow.
Once hydrated, the living cells of the pollen activate and begin to grow. The pollen cells form tubes that extend down the stigma toward the plant ovum. The pollen cells know in which direction to form the tubes by the direction from which they are provided water by the stigma. The sperm cells in the pollen then travel down the tubes to fertilize the ova.