  We introduce transverse momentum dependent parton distribution functions
(TMDs) for gluons with definite rank. The rank refers to the azimuthal
dependence corresponding to the tensorial structure in transverse momenta
multiplying universal functions only depending on $x$ and $p_T^2$. In this way
only a finite number of functions of definite rank remains for a target with
the maximal rank depending on its spin. Gauge links, required for color gauge
invariance, enter in the explicit description of the matrix elements
corresponding to these TMDs and account for their process dependence. In this
way a general gauge link dependent function is expressed in the universal set,
where all process (i.e. gauge link) dependence is isolated in gluonic pole
factors multiplying the universal TMDs of definite rank.
