We study the leading-power gluon transverse momentum dependent distributions (TMDs) of relevance to the study of asymmetries in the scattering off transversely polarized hadrons. Next-to-leading-order perturbative calculations of these TMDs show that at large transverse momentum they have common dynamical origins, but that in the limit of small longitudinal momentum fraction x only one origin remains. We find that in this limit only the dipole-type gluon TMDs survive and become identical to each other. At small x they are all given by the expectation value of a single Wilson loop inside the transversely polarized hadron, the so-called spin-dependent odderon. This universal origin of transverse spin asymmetries at small x is of importance to current and future experimental studies, paving the way to a better understanding of the role of gluons in the three-dimensional structure of spin-polarized protons.Scattering off protons in high energy particle collisions such as performed at RHIC and LHC, can be described as scattering off quarks and gluons inside the proton. As the energy of the scattering process increases, the gluons play an increasingly important role, as reflected by a fast growing gluon density inside the proton. The limit of high gluon density is the one in which the gluons carry only a very small fraction, x, of the longitudinal momentum of the proton. It is expected on theoretical grounds that the gluon density will not increase without bound towards small x, but rather that it will saturate. Because of the dominance of gluons over quarks and the expected gluon saturation, the description of scattering processes considerably simplifies in the small-x limit. A complication that remains in this limit though, is that gluonic effects do not manifest themselves in the same way in all processes.It has recently become clear that the transverse momentum distribution of gluons inside the proton is not a unique quantity. Different processes may probe different distributions and thus yield different answers. This has become apparent from studies of the unpolarized gluon distribution in the small-x regime [1-3] and, independently, from studies of spin effects in high-energy scattering processes. Scattering experiments involving a spin-polarized proton exhibit large asymmetries in the production of final state particles [4][5][6][7][8][9][10][11][12]. Theoretical studies of these still largely ununderstood single spin asymmetries (SSA) led to the insight that TMDs of both quarks and gluons are sensitive to the flow of the color charge of quarks and gluons in a process and hence that they are in general process specific, i.e. nonuniversal [13]. TMD studies of the color flow dependence are generally not performed in the high gluon density region. In [2,3], the two types of treatments were connected for the case in which neither the proton nor the gluons are spin-polarized. For transversely polarized protons the connection between the TMD and small-x formalisms has so far not been made. This is our aim here.We wil...