Why are triamino compounds so rare? I was doing a reaxys substructure search for the compound shown on the left below, with the 3 amines on 1 carbon. However, the closest I found were all trinitro compounds like on the right. I would have thought the nitro compounds would be less stable and likely to explode. But given the lack of triamine compounds, they must be hard to make. All I can figure is that when all three amines are protonated you end up packing a lot of postive charge in a small place.



Now that I look at that nitro structure I'm pretty sure I got the charges wrong. Just ignore that.
You may be familiar with the equilibrium that exists between a gem-diol and the corresponding carbonyl compound, as shown in the figure below.  The carbonyl double bond is very strong, so in most cases the equilibrium lies far to the carbonyl side.



The same type of equilibrium exists in the case of bis- and tris-amino compounds where all of the amino groups are attached to the same carbon atom.  In the case of such a tris-amino compound (see figure) the imino analogue of a carbonyl is generated, but since a third amino group is present, another equilibrium between the imino compound and a nitrile also exists.  Just like in the carbonyl case, the nitrile triple bond is very strong.  So when a tris-amino compound is generated an equilibrium with a very stable nitrile will be set up and the equilibrium will (usually) lie far to the nitrile side.  Most tris-amino compounds prefer to exist as nitriles.  If the amino group is fully alkylated (all of the amino hydrogens are replaced by alkyl groups), then this equilibrium cannot occur and such alkylated tris-amino compounds should be isolable.