The first one Chandrakaant was born as Khar. And the disciples of the three Braahman scholars were fourteen and they also became Brahm Raakshas. They were sent to fight with Raam in the beginning. On listening to Shoorpanakhaa, Khar came to know that Vishnu has incarnated in the form of Raam and thus he wanted to get released from his Shaap by being killed by Raam, and hence firstly he sends his 14 Raakshas, who were their 14 disciples, and later these three brothers also follow them and thus get released from their Shaap.

Khar Gets Shiv Ling
Taken from   Vaikom Temple site

Once Maalyavaan preached Shaiv Vidyaa Upadesh to Khar, so he went to Chidaambaram, and did severe penance and Tapasyaa for the attainment of Moksh. Pleased with his penance Shiv granted all the boons he asked, and presented him with his three great Ling. Assuring that he will always be present in them, Shiv disappeared. He asked Khar to worship the Ling to attain Moksh. When Khar was returning south from Himaalaya with the three Ling, he had one Ling in his right hand, another Ling in his left hand and the third Ling hung by the neck. He felt tired, so he kept those Ling on the ground and rested awhile. After resting when he tried to pick them up, they wouldn’t budge. He had realized that it was Shiv’s Maayaa, so he called unto him, the Heavens spoke - "I shall remain here giving Moksh to whom so ever take refuge in me”. Khar having attained Moksh entrusted the holy Ling to the custody of Maharshi Vyaaghrapaad who had followed him invisibly. Khar asked the sage to protect them and worship them.

Note
Who was this Maharshi Vyaaghrapaad? Is this the same Rishi who was living during the times of Guru Namashivaaya, Gihai Namashivaaya and Patanjali? OR there are two Vyaaghrapaad?

Belief is that the Shiv Ling placed by Khar by his right hand is being worshipped at Vaikom, the one in left hand he kept at Ettumannoor and the one hung by his neck, he kept at Kadathuruthy, even to this day.

The Ling carried by Khar with his neck is believed to be at Kadathuruthy and the one by his left hand is at Ettumanoor. The fact that the distance from Vaikom to Kadathuruthy and from there to Ettumanoor is more or less the same, gives credence to this legend. So the Darshan of all these three Ling on the same day is considered as good as the Shiv Darshan at Kailaash – the Abode of the Lord.

On a Vrishchik Krishn 8 (according to Malayaalam Era), Shiv appeared to Vyaaghrapaad with his consort Paarvatee. Shiv said - “This place shall be known as Vyaaghrapaad Puram”, and disappeared. The world famous Vaikkath 8th and all connected holy festivals are observed here even to this day on the same Vrishchik Krishn 8th.

Parashuraam Consecrated It a Temple
Vyaaghrapaad Rishi worshipped them for some time with great devotion, then he went away on pilgrimage. Months and years passed. One day Parashuraam Jee was going through skyway. He saw some good omens here, and saw a Shiv Ling emerged from water, he understood that it was the same Shiv Ling which Khar kept here. So he came down and consecrated the Shiv Ling here with proper rites. Pleased with his greatest devotee Vishnu (Parashuraam is considered Vishnu's 6th Avataar) Shiv and Paarvatee appeared before him and said to him - "From now on, I will stay here as Shaiv Vaishnav Chaitanya" and grant all devotees their wishes and Moksh." and disappeared

Full of joy Parashuraam Jee performed Shiv Ling Poojaa there for some days. Then he himself built a temple here and entrusted a noble Braahman of Taruna village whom he taught Shiv Poojaa Mantra. The Braahman learned all the 28 Shiv Aagam and wore Rudraaksh and Bhasm. Parashuraam donated the whole temple, along with Ling, to Braahman and disappeared. It is the belief that the temple and all rites and customs are planned and fixed by Parashuraam himself.