  In this paper the numerical solution of potential problems defined on 3D
unbounded domains is addressed with Boundary Element Methods (BEMs), since in
this way the problem is studied only on the boundary, and thus any finite
approximation of the infinite domain can be avoided. The isogeometric analysis
(IGA) setting is considered and in particular B-splines and NURBS functions are
taken into account. In order to exploit all the possible benefits from using
spline spaces, an important point is the development of specific cubature
formulas for weakly and nearly singular integrals. Our proposal for this aim is
based on spline quasi-interpolation and on the use of a spline product formula.
Besides that, a robust singularity extraction procedure is introduced as a
preliminary step and an efficient function-by-function assembly phase is
adopted. A selection of numerical examples confirms that the numerical
solutions reach the expected convergence orders.
