As you discovered, a model can have only one iterator, so you can not copy the contents of each submodel having an iterator into one bigger model. Instead, depending on your needs:
1) If the models are totally independed (one model does not create output for the next model), you can simply throw all (sub)models into a "master" model and click run. It will process the models in an arbitrary order, probably the one in which they get added. This doesn't matter in this case, since the models are independed.
2) If the models are depended (one model creates output for the next one), you need to expose its output parameters by right-clicking the last (output) parameters, and choosing "Model Parameter", this will expose your output parameters to the "outside world". If you now add such a submodel to the "master", it will show its outputs and you can "chain" the models by using the connector tool to chain the output of one model to the next.
3) If the models are not really depended but need to run in a prefixed order, you can use the connector tool to connect the output parameter of the first model, to the main model icon of the second model (not to an input parameter!), and choose Precondition. This will ensure the second model only runs after the first models finishes and has generated output.