Taylor (left) wasted no time in dismissing the challenge of Hine
Phil Taylor's bid for a 13th PDC World Darts Championship title gathered pace as he breezed past outsider Steve Hine.
The part-time baker from Coventry was outclassed as Taylor romped to a 4-0 win and progressed to the third round.
"When you are playing it doesn't feel easy, you try to win every leg," said Taylor. "I am happy to get through."
Co Stompe earlier surprised fifth seed Mervyn King 4-2, and will meet Mark Dudbridge, who needed a tie-break to edge out Alan Tabern 4-3.
Taylor, who has dropped just three legs in the tournament, hit six 180s and registered an average of 103.28 in a simple victory over Hine, who recently dropped full-time bakery work to go part-time and devote more effort to his darts.
It will be like Nigel Benn versus Chris Eubank, it will light up the tournament
Phil Taylor on a possible meeting with Adrian Lewis
A meeting with protege Adrian Lewis in the last eight is now a possibility for the 14-times world champion.
"Adrian has impressed me for a few matches now, he has been very, very good," said Taylor.
"If me and Adrian play in the last eight, I think you are going to see the winner (of the event) come from that match.
"I used to stand next to him and say do this, do that and now he is doing it.
"It will be like Nigel Benn versus Chris Eubank, it will light up the tournament."
Taylor will face Scotsman Robert Thornton, who beat Germany's Jyhan Artut 4-1 in Sunday's last tie, while Lewis will play Kevin McDine in the third round after both won earlier in the day.
Lewis saw off Wes Newton 4-2 while McDine whitewashed Barrie Bates 4-0.
Dutchman Stompe, who reached the quarter-finals of last year's competition, defied eight maximums from his opponent and ended the match with a three-dart average of 99.
"I know what Mervyn can do," said Stompe. "The way he plays in the practice room is unbelievable, but sometimes he can't always bring it on to the stage.
"When I missed those four darts at double top for the match, he came back with some fantastic finishing.
"But I managed to come through in the end and it feels great. If I play like that and take out my double opportunities when they come, I could go all the way."