...........
So, in this situation, Kid would time travel in one dimension and her actions would inevitably cause the split in 1010 AD. If Kid tried to time travel in 1020 AD in Home World, she would be instantly TB'd away once she passed the 1010 AD mark since Home World didn't exist before 1010 AD.
That is, of course, assuming that a "Y" branch theory is correct. But it certainly works and is logical, isn't it?
It all seems logical, except for one thing:
Timeline 1 should not have Kid appearing in 1010 AD. Kid does not travel until 1020 AD, Timeline 1, so she can't appear in 1010 AD in the same timeline. Therefore, given your scenario, Timeline 1 and Another World can't be the same if Kid appears in 1010 in both dimensions. This is how I think your situation should look:
Timeline 1 (pre-split, not considered Another World): ----------------------------Serge drowns in 1010 AD-----------------------Kid time travels at 1020 AD.
l
l
------------------------------------------------------------------------------------
l
l (Another)
Kid appears in 1010 AD----Serge still dies--------------------------- New Kid is TB'ed at 1020 AD
l
Dimensions Split-50/50 chance l
Serge is saved--------------------------- New Kid is TB'ed at 1020 AD
(Home)
So, the question that needs to be asked is this: Is Another World merely Timeline 1 extended out, or is it different entirely? I'm gonna go search the script, but I thought it was implied that Another World is just the extension of Timeline 1, the original timeline. If that were so, I think you'd have something like this, which is what prompted my theory (the bold goes to the DBT at Time Error X):
(Time Error X-6 months or so) (Time Error X)
Timeline 1 (pre-split, Another World): -----
Serge drowns in 1010 AD----Kid calls Serge:no response-- Kid travels to 1010-Dimensions Split l l
l l
------------------------------------------------------l--------------------------------------------------
l l
l l
(Home World) Kid appears in 1010 AD----Serge is saved---------------Serge crosses-------------------------New Kid is TB'ed at 1020 AD
(Time Error X) (Time Error X+10 years)
OK - now to the script to see if I can validate that Another World is in fact the original timeline.