Superphone

The superphone was the nickname Rose Tyler gave to her mobile phone after it was was altered by the the Doctor, giving it the ability to communicate through time and space. Similar "superphones" have been created by the Doctor many of his companions since Rose, and the Doctor has one of his own.

Abilities
The superphone the ability to make calls through time and space. They can also call in places where there should be no service for phones, either because it has not been invented, been outdated, or simply unavailable in a location. This enabled enabling Rose to call her mother Jackie while on her adventures with the Doctor. (DW: The End of the World) Adam Mitchell, allowing him to phone his mother in his own relative time. Unfortunatly, Adam used the phone in an attempt to bring knowledge of the future back to his own time, for self gain. This led to him being expelled from the TARDIS by the Doctor. (DW: The Long Game)

The Doctor also altered Martha Jones' phone in an entirely different way (using his sonic screwdriver rather than a technological addition to the phone) to function in a similar manner. (DW: 42)

Donna Noble's phone was enhanced later by the Doctor as well. (DW: The Doctor's Daughter)

Due to the danger at hand, the Doctor also altered Barclay's phone in order to get in contact with UNIT. What happened to it afterwards is not made clear. (DW: ''Planet of the Dead)

Examples of Use
During the Slitheen crisis, Jackie Tyler called her daughter on her superphone (first time in the series it was refered to as such) and it worked even in the sealed cabinet room. Rose's superphone was the only working phone in that room and it provided an outside line for The Doctor to communicate with Mickey Smith and Jackie and coordinate efforts against the Slitheen. Using the connection, the two groups figured out the Slitheen's weakness and The Doctor managed to talk Mickey through shooting a missile at 10 Downing Street, destroying the Slitheen. Later Rose recived a call on it from The Doctor on the TARDIS.

While stuck on Pete's World, Rose's superphone still worked and she used it to find out about that world. During the invasion of the Battersea powerstation, The Doctor had Mickey find a much needed code and he transmited it to Rose's phone via text. The Doctor plugged the phone into a nearby console and the code shut down the Cybermen's inhibitors, defeating them. The Doctor had Mickey keep Rose's superphone as it had the code he needed programed into it.

Rose later replaced her old superphone with a new one and while trapped on Krop Tor, tried to call her mother, but failed as Krop Tor for whatever reason had no service for her phone, even though the superphones can call anywhere in the universe, possibly because of the Beast trapped on Krop Tor or an invention of its imprisoners.

While stuck on a ship falling out of orbit of a sun, Martha's phone was modified by the Doctor to call her mother. Over the rest of the season she did this a lot, unaware that her calls were being monitored. While stuck on the ship and needing an answer, Martha called her mother to look it up on the Internet.

Following her ordeal during the "Year That Never Was", Martha Jones gave her phone to the Doctor (DW: Last of the Time Lords), in order to contact him should he ever be needed; he kept it with him and was called (by Martha), bringing him back to Earth to assist with UNIT's investigation of the ATMOS facility. (DW: The Sontaran Stratagem)

Martha's phone was also used by Torchwood, Mr Smith and Harriet Jones, all utilising the Cardiff rift to contact the Doctor when Earth was teleported by Davros to the Medusa Cascade. (DW: The Stolen Earth)

When he was stuck on San Helios, The Doctor modified Barclay's phone into a superphone to communicate with UNIT on Earth. The Doctor used it to communicate with Doctor Malcom Taylor and Captain Erisa Magambo to try to find a way back and deal with the possible threat. Even though his phone was unmodified, Nathan was able to call The Doctor on the superphone with it, showing that any phone can call a superphone no matter where they are. The Doctor was succesfully able to bring the people on Bus 200 home, and used the phone to tell Malcom to close the wormhole despite being hung up on twice (something that surprised him). What happened to it afterwards was left unclear. (DW: Planet of the Dead)

Apparently Lady Christina de Souza either learned of the Doctor's superphone number, or obtained Barclay's phone, as at one point the Doctor answered his superphone in the TARDIS thinking, momentarily, that it was Christina calling him (it was actually Martha). (IDW: Tesseract)

Strengths and Weaknesses
The superphone has the ability to call the person you're looking for no matter where in time or space they are, refered to as "free roaming", and even locks onto the the user's relative time (would you normally have been in 2004, the phone will call from that time); the only exception to this last rule is the Doctor himself. It even works in areas of no service, as proven when the Doctor, Rose and Harriet Jones used Rose's superphone to communicate with Jackie Tyler and Mickey Smith while trapped in the cabinet room, something that is usually impossible. (DW: World War Three)

However Rose could not get any reception on Krop Tor (DW: The Impossible Planet) implying that the process is somehow related to the TARDIS, or that the blackhole was running interference or because of The Beast on the planet, which caused a lot of impossible incidents and coincidences. Martha also found trouble contacting the Doctor when the Earth forced out of sync with the rest of the universe, as she found that her phone couldn't contact the superphone(DW: The Stolen Earth) but this was probably because the Daleks were blocking all interstellar transmissions, since Wilf and Sylvia could not contact Donna's superphone with their normal phone and Rose Tyler's superphone was also non-functional.

Also, when the Doctor modified Donna's phone, he was able to call Martha on it depite her being on another planet than Earth and the phone she was using being an ordinary cell phone. Also when he used Barclay's modified phone, Nathan was able to call him despite being on the same planet as he was. This indicates that any phone can call the superphone or can be called by it no matter if it has service or not.

Prototype
The Fifth Doctor and Nyssa created an experimental device called the "Temporal Interocitor" to communicate across spacetime. This device is strongly suggested to be the prototype for the superphone. (BFA: Renaissance of the Daleks)