Niobe revealed the origin of the fragments during the first event (I assume that the same information was revealed to the Machine and Merovingian organizations by one of the Agents and either the Merovingian or Flood). Quote ...
"It looks like Neo made certain changes to the Matrix while he was here. We're
not sure why or what they're supposed to do, but the Machines have discovered it
too. As you can imagine, they're not happy about it.
The Machines are throwing all their best code breakers at it. But now we think that
by dismantling the programs Neo put in place they've triggered a failsafe.
Neo's residual programs are fragmenting, but we think that's what they were
designed to do. The fragments are flowing through the Matrix now and it looks to
some people like they might have left us a message or maybe even a weapon.
What we need to do now is find these fragments and discover what they really are
and what they really do.
It's a sure bet the Machines and the Frenchman will also be gunning for these things
so watch yourselves. The truce isn't going to mean a thing when you cross paths
and you all want the same scrap of code.
We also have another problem - there's another group out there too. They seem to be
marked by bright lights but they can disguise themselves - be careful.
As far as numbers go we need as many as possible.
If you get one of the special fragments we have a series of clandestine drops set
up on the streets of the Matrix - get your frags to one of these collectors and they'll
give you some additional resources that you can use to keep looking for more.
I know some of you may have heard other things on the street from Captain
Morpheus but I urge you to stick to the facts as I have outlined them to you here.
Ok that's enough standing around - get out there and hit the streets people - there's
no time to waste!"
It seems the fragments had little to do with any Neo/Smith merger. The Machines found what Neo changed, try to dismantle it, and triggered the failsafe that caused what Neo did to fragment and be spread throughout the city where the false Agents got their hands on it.