The public cloud for software-as-a-service offerings, including back-end business services is catching fire, and Amazon and Google, which already run extensive public clouds, are well positioned to dominate in the arena. That’s despite Dell’s recent purchase of EMC, say the experts, because the two companies under EMC — VMware and Pivotal — although they are cloud computing companies, are not big players in the public cloud. Cloud platform services are expected to become a $44 billion market by 2020.

That is just one of the findings of a Forrester Research report, says Wired, about the future of the cloud computing business, which it deems a “hyper-growth” market predicted to be worth $191 billion by 2020. “The adoption among cloud among enterprises, which is really where the money is, has really picked up steam,” says analyst John Rymer. “It’s a big shift. The cloud has arrived. It’s inevitable.”

It’s already a big market. Amazon says its cloud operation is now worth $4.6 billion and expected to grow to $6.23 billion by the end of 2015. Microsoft is the second biggest company on the space, with stated revenue of $6.3 billion this year, including sales of its Office 365 and its Dynamics customer relationship management service. Google has been slower to market, and IBM is also a player since it acquired SoftLayer.

But Forrester downplays the potential of Dell, even after its purchase of EMC for $67 billion because its VMware and Pivotal are focused on private cloud solutions. Amazon’s EC2, which allows companies to build and run their own software, is the future, says Forrester. By 2020, back-end business services are expected to be worth $14 billion, and cloud software applications $131 billion.

Rymer says that the public cloud won’t take over the entire IT market, but this is where we can expect to see growth, with Amazon taking the lion’s share. “They have a massive customer base and [they’ve] been at it longer than anyone else,” Rymer says.