DBTC is based on "theoretical" exponential distribution of a coral.
ie, I have a frag that i give to person1
(1 frag in pool)
Person1 grows out frag and gives to persons 2A,2B,2C
(3 new frags in pool)
Person 2A gives out frags to persons 3A,3B,3C
person 2B gives out frags to persons 3D,3E,3F
Person 2B gives out frags to persons 3G,3H,3I
(9 new frags in pool)
Of course, frags die, people don't pass on etc. ..plus we don't have dozens of people (yet!).
Now, if you recieve a DBTC coral, you are more than welcome to start up your own chain of a new coral, but there is no obligation beyond growing out the frag you received and passing on it's children.
Torches (heck, most corals) have an induction period and then grow fast (under reasonable conditions). I started out with one head and in 2 years, I had 6 heads.
Same with a frogspawn and ended up with about 9 heads. With LPS, keep an eye on your Mag. You can spot feed with small food too and growth can accelerate a fair bit.
Some frags grow slow and some fast. Zoas for example, can potentially double or triple in as many months, while some SPS take as many years. You jsut do what you can to keep the coral healthy