Hecate is probably the first TRIPLE GODDESS and sense the beginning, has been a Patroness of all Witchcraft and Magick.
 She is the Goddess of the cross-roads; and is said to be supreme, both in heaven and hell. She has three faces which are turned in three directions. One face is that of a Dog (Maiden), one of a Horse (Mother) and one of  Snake (Crone). She is usually seen with two ghost hounds that were said to serve her. her name was cried at midnight at the cross-roads of cities to win her favor. She is a goddess of the Underworld and companion of Persephone.

     It is said that great honor comes to him whose prayers Hecate receives favorably. Zeus did not take away her privileges or anything that was her portion  after he defeated the TITANS , instead she was aloud to keep what was her own, as was in the beginning. This means that Zeus, Poseidon and Hades have no power over that which is hers whether it resides in there Kingdoms or not. Hecate is also guardian of the keys to the Underworld

During war Hecate gives victory and  glory to those who have one her favor . She is also said to make the small heard great or the great herd small, according to her will.

There are three versions of Hectare's parentage (3 seems a very fitting number)

1. TARTS & Night

2. Presses & unknown  (Presses is the Titan Son of CRUISE and EURYBIA)

3. Presses  & Aster (Presses is the Titan Son of Crius and Eurybia)  (Asteria Daughter of PHOEBE and COEUS (ceus) of  sister of  Leto)

Personally I feel that Tartarus is the logical choice for parentage, especially since Zeus, after his defeat of the Titans "aloud" Hecate to keep what was hers since the beginning. That choice, that Zeus made only makes sense if Hecate was the Daughter of Tartarus and therefore predated Zeus. besides zeus would not want to anger Tartarus by causing his Daughter any harm, seeing as how Tartarus was helping to keep bound ALL of the Titans.

Eurybia :  Titan Daughter of Oceanous and Gaea, called flint hearted by Hesiod and the Mother of  Lucifer

Phoebe : The Titan daughter of Uranus and Gaea. Older version od Diana the Moon Goddess Mother of Asteria and Leto. GrandMother of  Apollo and Artimis. She wore a wreath of Gold.

Coeus :  titan son of Uranus and Gaea Titan of Intelligence. Father of Leto.

Tartarus : Cosmic Place. Tartarus is the lowest abyss beneath the earth where all waters originate; all rivers flow into the chasm of Tartarus and flow out of it again. Tartarus is, they say, a gloomy place as far distant from earth as earth is from the sky. For, it is said, a brazen anvil falling down from heaven nine nights and days  would reach the earth upon the tenth: and again, a brazen anvil falling from earth nine nights and days would reach Tartarus upon the tenth. Still others say that  Tartarus yawns deep under the shades, extending down twice as far as the view upward to Heaven. Tartarus and the Underworld are the realm of Erebus, which is pure Darkness. Tartarus, the Being.

   Tartarus is, at the same time, a being capable of intercourse. Tartarus is the father of such monsters as Echidna and Typhon . Erebus, the Darkness of the Underworld, possibly existing from the beginning together with Chaos, Nyx (Night) and Tartarus, gave birth, according to some, to the Moerae, the Hesperides, Hypnos (sleep), Geras (Old Age), Thanatos (Death) Styx and Hecate.

After mentioning LUCIFER  earlier in this page, I felt compelled to add just a little more about him:
Lucifer : Also called Eosphorus ,Hesperus , Phosphorus and of course; Lucifer. Lucifer is the morning and
evening star (Venus).  Again we get 2 conflicting accounts of LUCIFER'S parentage:

1. ASTRAEUS and EOS
 

2. EURYBIA and Unknown.

Eos: Is the Dawn.  Parentage: Hyperion & Thia