A statistical theory of finite-sized aggregates and domain structures in dilute solutions of amphiphilic macromolecules (homopolymers or copolymers) is developed. A minimalist model involving, essentially, two types of chemical groups (insoluble H and soluble P) is studied in the regime where polymer tends to phase separate, forming rather dense amorphous particles with low Surface energy. The surface tension and the elastic bending moduli of the polymer/solvent interface are obtained and are related to the molecular parameters. The Gaussian modulus kappa(G) is predicted to be negative; typically vertical bar kappa(G)vertical bar is smaller than the mean bending modulus kappa(2). It is shown that the condensed polymer phase can remain dense, homogeneous, and stable with respect to microphase separation even as the surface tension decreases down to zero (or below it). Stable large aggregates of well-defined size are predicted in this regime. The size of aggregates and their shape depend on surface tension gamma, the spontaneous bending modulus kappa(1), and the ratio kappa(G)/kappa(2). We show that bicontinuous morphologies (rather than colloidally stable polymer mesoglobules) are thermodynamically favorable for small vertical bar kappa(G vertical bar). We present a quantitative argument showing that the gyroid structure is more favorable than other bicontinuous morphologies (primitive cubic and double diamond). The gamma-kappa(1) phase diagrams showing the regions of stability of different morphologies are obtained. Two types of spherical rnesoglobules are predicted, namely equilibrium and metastable globules whose sizes are shown to be essentially different: they depend on kappa(1) in qualitatively different ways. Recent experimental data on mesoglobule formation in solutions of thermosensitive amphiphilic polymers are discussed in the theoretical light.