"vastly distributed" is correct and usable in written English.
It means that something is spread out over a wide area or to a great number of people. For example, "This charity's resources are vastly distributed around the world to help those in need."
Unfortunately, the DNS ecosystem has slowly evolved from a simple system at its inception to a vastly distributed, complex and brittle system today.
But long term we think of ourselves as more of an enabler of the future of work — of an environment where every company could be working with a vastly distributed talent pool, everywhere in the world.
Establishing frequent employee progress meetings is essential in vastly distributed groups with less frequent informal communication.
For a start, Harari suggests, it is destined, if current trends continue, to be vastly unequally distributed.
Yet for a relatively small figure the surface station could be vastly upgraded and better distributed.
And even though we are devoting resources to thermonuclear fusion, we have no comparable programs for solar power satellites or vastly expanding the electric distribution grid, for distributed solar energy.
However, hospitals and health facilities are limited in number, inadequately distributed, operate using vastly different standards and often cannot provide a minimum package of primary healthcare (PHC) services.
Those systems are designed to protect utility workers when they're fixing supposedly dead lines, but will vastly complicate the job of achieving distributed generation.
In this paper, an algorithm is presented that converts a system generated from FEM into the state space model of an interconnected system, thus vastly reducing the complexity of synthesizing a distributed control strategy.
In fact, the text of Larijani's presentation, which was distributed to the audience, was vastly different from what he said at the meeting, a subject that astonished many.
As a result, computers with vastly different software systems can participate in the same distributed system, simply by conforming to the message protocols that govern the system.
