There was nobody outside that night to see Belthazor chasing little twelve year old Piper Halliwell, intending to kill her. It was perfect.
Piper was scared. She couldn't stop and use her power on him, that would just give him the perfect moment to kill her. Too late, she was about to hit a wall. He would surely kill her if slamming into a wall didn't.
She turned to look behind her, see where he was, not caring if she hit the wall because she was going to die anyway. But the thud never came. She had run right through the wall and was now... still in San Francisco. She stopped a few feet away from the wall, confused and in shock, but started running again when she heard Belthazor run through after her.
As she rounded the corner, she stopped again, realizing he wasn't behind her anymore. She poked her head around the building and saw him standing, more confused than she had been. She decided to use her power then and there and froze him. Then she ran off in search of her house.
On the way, she met a police officer named Darryl. She asked him if he knew where Halliwell manor was. He said he was on his way there now and if she needed a ride to hop in the car. She did, trusting this man wasn't a demon.
They reached the manor in about fifteen minutes. It looked the same as ever. Until Piper saw who lived there. Darryl rang the bell and all three sisters, Prue, Phoebe and older Piper, answered. When young Piper realized what had happened, they were already inside and the sisters wanted to know her name. "Uh... Penelope," she said, using her grandmother's- and their's too- name.
"Nice to meet you," said Phoebe. "Are you new to the city?"
"Yes."
"Do you need a place to stay?" asked Prue.
"I guess so."
"You can stay with us. Come on, let's find you a room," said older Piper, holding out her hand. Young Piper took it and they went upstairs. They found a guest room for her to stay in. She decided to rest for a while, after having a tiring trip. Well, at least it was partly true.
In her room, she thought about how she could have been transported to an alternate dimension that was in the future. She came up with nothing. Later, she would tell the sisters everything. For now, she needed rest.
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Belthazor awoke from his frozen state in the middle of the night. He decided to take human form and find a hotel, then search for the witch in the morning. His human form was Cole Turner. He had no idea where he was or how. He also didn't know there was another one of him here in this alternate world.