You don't have to absolutely read RoboRose, but it is recommended for better understanding. Plays somewhere between the end of DW season 3 and before TW ending season 2.
The Torchwood team had been very busy with eating piz-... ehm... working, when suddenly the hub door opened. Everyone stared open-mouthed at the intruder.
Jack stepped forward, disbelief evident on his face.
"Hey, Jack. Sorry to interrupt, but I have a very urgent business with you lot." He drew a big blaster out of his pocket. "I'm so very sorry but... I have to kill you!" He grinned at them. "Have a nice day!"
Everyone was frozen on the spot, unable to process what was going on, when suddenly another voice sounded from the door.
Jack's mouth began to hurt from all that gaping (and not in a comfortable way...). "Rose?! But you are... How can you be here?!"
Rose winked. "You ask me? For being dead, you are looking pretty good..." She turned to the Doctor. "Seriously, I can't let you alone..." She shook her head and opened (!) the Doctor's head.
The Torchwood team gasped at the sight. "He is a robot!" Owen screamed and for being a doctor, he looked remarkable disgusted.
"Yeah, yeah..." Rose pressed some buttons and closed his head again.
The Doctor blinked a few times,looked at the others and asked cheerfully, "Good evening, Lords and Ladies. Are you thirsty or hungry? Could I temp you with one of my fabulous massages?" He wiggled his eyebrows.
Gwen looked very tempted... "Well, actually..." She caught Jack's look and sighed. "No, thanks."
"Rose, what's going on here?" Jack felt exactly like that time on the Gamestation... when he woke up after being exterminated: confused and unexplainable randy.
Rose smiled at him. "May I introduce? This is DocBot V 2.0... V 1.0 sadly had an accident. He was more like the real Doctor, than he should have been after all... licked an electric power line. This one-" She patted his shoulder. "Doesn't have the oral fixation... which is a pity, really." She looked suddenly like she remembered really good times and sighed wistfully.
Jack's mind worked overload. Images appeared in his head involving two Doctors, one Rose, him and a lot of chocolate cream. He cleared his throat and tried (in vain) to get his mind out of the gutter. "And... and where is the real thing?"
"I'm here, I'm here!" The Doctor stepped out behind Rose. "Sorry, RoboRose is faster than us so I send her after him. She has DocBot better under control, anyway..."
"Yep, that's me!" RoboRose held up a hand and then turned to DocBot to give him a hug, which he returned lovingly. "I'm RoboRose 2.0... 1.0 was overused by the Doctor, since he-"
The Doctor put his hand on her mouth and hushed. "He, he he... I let her clean too much..." He coughed and blushed, asking himself if it was too late to search for his missing dignity...
Jack looked absolutely gob smacked by now. "Doc... You are a very dirty old man... I can understand that you built a robotic Rose, but another you... and then as a pair... I didn't picture you being a voyeur."
The Doctor was visibly confused. "Wha- ... Oh, no! You got it all wrong! I first only had RoboRose but then, Rose came back and after a while... she thought it was unfair that I had a robot her, so she wanted a robot me. Ergo: I built DocBot. And naturally, those two robots took a liking to each other, so-"
"Doc!" Jack interrupted his torrent of words. "Where is Rose, then?"
"Here!" The real Rose came panting through the door. "Sorry, but I'm neither a robot, nor have I a respiratory bypass system." She glared at the Doctor. "Couldn't you have parked nearer to the hub?"
He ignored her. "I'm really sorry about this, Jack! I wanted to change his software and accidentally activated the 'Kill Torchwood'-mode... Small mistake, really. Won't happen again!"
Jack glared at him. "Why does he have one in the first place?"
"Weeell, I was kind of... maybe a little... ehm... intsy wintsy bit alien drugged, when I built him?" He shrugged. "Not to mention the repressed rage I had for Torchwood. They took Rose from me, after all..." Rose kissed him on the cheek for that.
After trying to sooth those little shagging figures in his head, Jack asked, "How come you are here, Rose? I thought, you were trapped in a parallel world?"
"Oh, I found a way back. Not important now." She went to hug him. "Good to see you, Jack."
He grinned. "Yeah, you too." Under the Doctor's glare, he tried desperately to keep his fingers to himself. The images in his head, now five persons (including him), were still very vividly going at it like rabbits.
The Doctor clapped his hands together. "Alright, that's that then. We are going back to the TARDIS for some maintenance now... You can come with us, Jack, since you will probably want to catch up with Rose..."
Jack's mind (and libido) cheered at that prospect. He said good-bye to his team and went like a happy little puppy after the Doctors and Roses.
The remaining team members stared after him. Owen was the first to find his voice again. "Does he have any friends who are actually normal?!"