A fundamental example of pattern formation under far-from-equilibrium conditions is given by the famous diffusion-limited-aggregation (DLA) model, introduced by Witten and Sander in 1981. This growth model was shown to be the basic mechanism for the formation of complicated, fractal patterns in a variety of chemical, biological and geological systems. In this talk I will introduce a generalization of DLA to a wide family of 2d growth models, limited by transport processes which are not necessarily diffusive. This progress is enabled by combining two recent developments: (1) The Hastings-Levitov formalism (1998), expressing DLA as an iteration of conformal maps , and (2) The application of conformal map methods to solve a wide family of transport equations (Bazant 2003). The theoretical and computational advantages of our formalism will be demonstrated through a new growth model, namely an aggregation process limited by an advective-diffusive transport (where advection is controlled by a potential flow). This model is important in particular for studying aggregation processes in porous media exposed to underground flow over geological time scales, and may also be useful in capturing certain features of growth of bacterial colonies.