We study the complete phase diagram for a model of a binary mixture of two interacting polymer species A and A＇, each of fixed architecture (dendrimer, star, linear, or regularly branched polymer, brush, etc.) and size given by the number hi (or M＇) of monomers in it, on a lattice of coordination number q. For M＇ = 1, the model describes a solution. Branchings, if any, are regular in these architectures. This feature alone makes these polymers different from polymers with random branchings studied in the preceding paper [J. Chem. Phys. 108, 5089 (1998)]. Then exists a theta point regardless of the fixed architecture, which is not the case for random branchings. We identify this point as a tricritical point T at which one of the two sizes M and M＇ diverges. Two critical lines C and C＇ meet at T. The criticality along C corresponds to the criticality of an infinitely large polymer of any fixed architecture, not necessarily linear. This polymer is a fractal object. We identify the relevant order parameter and calculate all the exponents along C. The criticality along C＇ is that of the Ising model. Connected to T is a line t of triple points. The above results are well-known for a solution of linear polymers which we have now extended to a binary mixture of polymers of any arbitrary but fixed architecture. Our results show that regular branchings have no effects on the topology of the phase diagram and, in particular, on the existence of a theta state. The critical properties are also unaffected which is a surprising result. We point out the same subtle difference between polymers at the theta point and random walks as was found for a very special class of randomly branched polymers in the preceding paper (see the text). The behavior of a blend of a fixed aspect ratio a=M/M＇, M-->infinity, is singular, as discussed in the text.