I recently started watching Doctor Who (onto season 3) and noticed that the first time Rose traveled in the TARDIS and returned to her present timeline it had been about a month since she left. The Doctor always seemed to return Rose to the present day in her timeline when going home. How fast does the timeline of present day Earth accelerate when one is time traveling in the TARDIS? Secondly is the device attached to her cell phone always stuck on the last day she was present on her timeline when she makes a call?
As far as I can tell, the Doctor could take her home a day before she left, if he felt like it. There are very few constraints on what is possible.
Though initially angry at Rose (the Eccleston season), once he was in the thick of it he was prepared to manipulate time and sidestep the paradox by giving her father back to her. The only absolutely boundaries seem to be those imposed by other beings as powerful as himself (other Timelords, the Daleks, perhaps a few others).
If he drops her off weeks later in her own timeline, it's mostly that he can't be bothered to be more precise.
The TARDIS is a time machine, it can travel to any point in space and time. There is no dependency on where is left or is going to. The vagaries of the TADIS and the pilot's abilities may limit the precision of this.
The pilot may of course decide to return to a location with the same people at a slightly later time to avoid an individual meeting themselves.
Newer stories have introduced some specific restrictions, but that does not change the basic ability.