Amazon Web Services holds a 45 percent share of the worldwide public market for Infrastructure as a service (IaaS) — greater than Microsoft, Google and IBM’s shares combined, according to a quarterly analysis by Synergy Research Group.

AWS also leads in the platform-as-a-service (PaaS) market, though by a narrower margin, Synergy found. Only in the much smaller realm of the managed private cloud does AWS yield to market-leader IBM.

Microsoft and Google are each growing their cloud revenue at over 100 percent per year. Still, AWS remains twice the size of those companies, plus IBM, when it comes to IaaS, Synergy estimated. (Because Microsoft and Google don’t provide precise numbers, only estimates are possible.)

AWS posted $3.2 billion in revenue last quarter, up 55 percent year-over-year, and accounted for nearly 10 percent of Amazon’s company-wide revenue of $32.7 billion.

Profits from its cloud computing arm has fueled the rest of Amazon’s sprawling business and global ambitions.

Synergy’s study also found that some second-tier companies are seeing strong cloud computing growth, including Alibaba in IaaS and Oracle in PaaS.

Competition is tighter in the PaaS space, though AWS’s revenues there are nearly equal to those of its three main competitors in that segment: Salesforce, Microsoft and IBM. Though public IaaS is the biggest of the three main cloud segments, public PaaS is growing much more strongly. The database, IoT, and analytics sub-segments within PaaS are all growing by 100 percent or more per year, Synergy said.

In the managed private cloud segment, IBM is the market leader, followed by AWS, Rackspace and Australian firm NTT Communications ICT Solutions.