please specify what exactly You are reffering to because at the moment the question is very broad.
Generally speaking a complex formation is a bond formation where 2 species
a+ a electron deficient one from one side
and
b- a electron rich from the other side
forms a-b this is the case for solvatation, transition metal complexes etc.
But of course there are some considerations here:
for reaction: a+ + b- --> a-b to take place both a+ + b- must be somewhat stable in a solution state so they can react in a predictable, repeatable and at least somewhat pure fashion.
So any a+ species must be stable in a soluion: lets consider 2 options
a metal ion if its positively charged and a non-metallic ion if its positively charged
for example it is very well known that NaCl dissolves in water forming Na+ ions, thus sodium ion is stable in water, but it is unknown for lets say F+ or Br+ or O+ or any other non-metallic species to be stable in any solutions (few exceptions will be listed at the end) because generally speaking they will be so reactive that these species do not exist for a long time to make use of in our general chemistry, esecially forming complexes. (for now lets disregard carbocation chemistry).
Similarly any b- species must be stable in solutions, taking the example of NaCl, obviously Cl- ion is stable in solutions, similarly for example HO- , F-, R2N- etc. are well known to exist in the solution (provided the apropriate solvent) on the other hand any M (metal) negative ion M- would be unstable in solutions.
Thus we can conclude that the vast majority of positive species will be metals and the vast majority of negative species which are stable in the solvents available for us will be non-metals.
Next would be the consideration of octet rule (which shows why exactly the above mentioned species tend/tend not to to exist) or the filling of d orbitals for transition metal complexes but these can be looked up everywhere.
Now lets cnsider what would a complex look like : technically it could look either an(b) or (a)bn where n is the number of ligands. So either the electron deficient species (generally a metal considering everything we mentioned above) or electron rich species (generally a non-metallic element) would have multiple ligands.
In vast majority of cases b- would be negatively charged with 1 electron (-1), because the more negative species You construct the more unstable they get, this is the reason that Me-Li exists but H2C-Li2 does not (if we consider monomers). Organic/inorganic/ionic solvent we have available would not stabilize these species.
On the other hand species from electron deficient group could easily have a charge +3 (e.g. Fe3+) this is not because the species would technically be more stable, but because the stabilization in any solution (or solid) would occur via the electron pairs of the solvent or solid (assuming You use polar solvents to dissolve a salt - which You thechnically would have to do - disounting Kraun ethers).
So overly simplifying a could have multiple positive charges but b would generally have one negative charge, So a complex with an electronically deficient species would have a metal in its core, because the metal is generally a positive species.
Of course there are exceptions: for example 1 Cl- ion can act as an X type ligand for one metal and an L type for the metal next to it.
The whole Boron chemistry rests on B+ species, and N+ as in ammonium species have this tendency. Then again these 2 somehat large groups of organic ions are based on a positive species in the middle, stabilized by an abundance of negative species around them.
But as we dont have solvents which are positively charged (all sovents we have are very rich with electron clouds) and lacking in electrons which could stabilize b2- or b3- species then we have to do whith the positive species as the center.
So this could be an verly general answer to the question.