The pterosaur to bird theory contains two basic ideas, that differ from current mainstream thinking.
The first idea is that pterosaurs developed into a set of primitive bird lines.
The second is that EACH ONE of those primitive bird lines then developed into a set of corresponding modern birds, in what might be called a set of "parallel lines".
Seabirds (Ichthyornithes line)
- Pterosaur (Ornithocheiroidea) eg. Pteranodon -->
- An Ichthyornithes subgroup -->
- Gulls, Skimmers (Charadriiformes/Lari)
If any of this is not clear, I invite questions and comments.