I'm a tad confused about the sublink_mpb trees in TNG.
I downloaded all such trees from TNG100-1 and TNG300-1 at z=0, specifically with the field primary_flag=1, i.e. containing only central galaxies. By plotting the central halo mass (Group_M_Mean200) and stellar mass (SubhaloMassType[:,4]), I've recovered the expected mass relation for centrals at z=0.
At different redshifts, however, there are a number of subhalos which lie under the curve. These are clearly not primary objects (I've checked), but I specifically downloaded the main progenitor merger trees, specifically with the primary flag as an argument, so I don't see why there are non-primary objects in the trees. Shouldn't these progenitors predominantly lie on the main sequence at all snapshots?
Have I really got only the primary progenitors of central galaxies at z=0? Are they allowed to drop in stellar mass like this at earlier snapshots, and if not, what am I doing wrong? I'd really appreciate your help.
Unfortunately I can't see the images you uploaded. Can you provide one or two example IDs of TNG100-1 centrals which have strange behavior?
Your selection is correct, you've picked centrals at z=0. As you say, I would expect the subhalos along the MPBs of those z=0 objects to be predominantly centrals, but this certainly isn't a strict requirement.
Two instances come to mind where this wouldn't be true: (i) a "fly-by", so the object goes central -> satellite -> central by z=0. Or (ii) a roughly equal mass (i.e. major) merger. Around the time of the merger, you have two roughly equal mass subhalos, so the definition of which is a central and which is a "satellite" is ill-posed, and so you could again have central -> satellite (during the merger, together with an apparently large but artificial mass dip) -> central.