  We study the structure of scalar, vector, and tensor currents for on-shell
massive particles of any spin. When considering higher values for the spin of
the particle, the number of form factors (FFs) involved in the decomposition of
the matrix elements associated with these local currents increases. We identify
all the fundamental structures that give rise to the independent FFs,
systematically for any spin value. These structures can be conveniently
organised using an expansion in covariant multipoles, built solely from the
Lorentz generators. This approach allows one to uniquely identify the terms
which are universal and those that arise because of spin. We derive counting
rules which relate the number of FFs to the total spin $j$ of the state,
showing explicitly that these rules match all the well-known cases up to spin
2.
