Mr Light wrote:
Since they rebooted the universe in "The Big Bang", I have no idea what happened or didn't happen anymore... but in the RTD Era, didn't all the Daleks come from the single Emperor who fell out of the time lock?
Nope. Only the ones from the end of Series One.
Here's a brief history of post-Time War Daleks:
0. At the end of the Time War, the Doctor uses a weapon called "the Moment," incinerating the Daleks and Time Lords alike. The Time War itself has been "time locked," and the Daleks and Time Lords are largely erased from history, though advanced civilizations capable of detecting temporal alterations retain knowledge of them.
1. A single, standard-issue Dalek somehow survived the Doctor's use of the Moment and escaped the time lock, and was transported to mid-20th Century Earth in a weakened state before ending up in the collection of Henry Van Staten in 2008, when Rose Tyler touched it. It later committed suicide upon realizing it had absorbed some of Rose's DNA. ("Dalek" -- original date cited as 2012; I conjecture that it was actually 2008 and the Doctor just misread the year-o-meter in the TARDIS again, to correct for no one knowing what a Dalek was in a supposedly post-Dalek Invasion timeframe.)
2. The Emperor of the Daleks -- who apparently replaced or overthrew Davros as Dalek leader early in the Time War -- also somehow survived, and escaped the time lock. The Emperor ended up in the 2,001st Century, and enacts a centuries-long plan to manipulate the Fourth Great and Bountiful Human Empire through the use of mass media while using Human refugees and dissidents as raw material to create a race of Daleks with Human DNA elements who will worship it as a god. The Emperor and its devotees are all vaporized by Rose Tyler upon her return to the 2,002nd Century from 21st Century Earth. ("Bad Wolf"/"The Parting of the Ways")
3. During the war, the Cult of Skaro entered the Void in a specialized ship while escorting the hijacked Genesis Ark, a specialized Time Lord prison ship containing hundreds of Dalek prisoners of war. The Cult of Skaro escapes the Void in 2007 Britain, unleashing their liberated forces upon the occupying Cybus Cybermen army before the Doctor and Rose are able to suck them back into the Void. The Cult itself uses an emergency temporal shift to escape to 1930s New York. ("Army of Ghosts"/"Doomsday")
4. The Cult of Skaro, numbering at only 4 -- the last remaining Daleks in all of time and space -- enact a plan in 1930s New York to create Human/Dalek hybrids. This plan is thwarted when the Cult turns on its leader, Dalek-Sec. The only survivor is Dalek-Caan. ("Daleks in Manhattan"/"Evolution of the Daleks")
5. Using his emergency temporal shift, Dalek-Caan attempts a suicidal run into the time lock -- and, amazingly, succeeds in penetrating it. He thereby rescues Davros from an early point in the Time War. Davros and Dalek-Caan, now driven mad, escape to the Medusa Cascade of the early 21st Century. From there, Davros uses his own tissue to create a new Dalek army with Kaled DNA elements. In 2009, this new Dalek Empire invades Earth and abducts numerous planets in an attempt to active a Reality Bomb that will wipe out all matter excepting their own, but are thwarted by the Doctor and his friends, who use Dalek technology to destroy all Dalek ships and forces... ("The Stolen Earth"/"Journey's End")
6. ... except for a single ship with a handful of Davros-tissue Daleks. These Daleks eventually located a Progenitor Device on 1940s Earth, which they use to create a new set of genetically pure Daleks (referred to as the "New Dalek Paradigm"). These new Daleks immediately exterminate their Davros-contaminated creators before escaping into the past from the Doctor. From there, they re-establish Daleks into history, creating a new Dalek Empire. This timeline's Dalek Empire eventually allies itself with the Shadow Proclamation, the Sontaran Empire, and the Cybermen in an attempt to trap the Doctor in the Pandorica to avert the destruction of reality by the explosion of the TARDIS on 23 June 2010; this Empire is also the one from which the Doctor stole information on the Silence, and which recruited the Doctor to help destroy its Asylum. ("Victory of the Daleks," "The Pandorica Opens," "The Wedding of River Song," "Asylum of the Daleks")
In other words, the Dalek Empire that exists today can trace a direct line to Dalek-Caan of the Cult of Skaro for its survival. Dalek-Caan escaped the Time War in the Void, Dalek-Caan rescued Davros, Davros created his genetically impure army, some of the Davros-contaminated Daleks found a Progenitor Device, the Progenitor-created Daleks went back in time to found the Empire that exists now. So what happens now is, the Progenitor Daleks have now re-established themselves into history, but the Time Lords remain erased from history.