Wow. Firstly, I had not realised the scenario was supposed to represent the expansion of the universe, and secondly, KALSTER's recent replies are actually describing accelerating expansion, rather than constant expansion.
Firstly, we cannot use the relativistic velocity addition formula for this.
Secondly, when cosmologists refer to constant expansion (which is the state between an accelerating and a decelerating universe), it means that objects recede at a constant speed (which is actually how zinjanthropos described the scenario), NOT that the hubble parameter remains constant. This is important, because it means that we can see galaxies who have always had recession speeds faster than light.
Even as the expansion of the universe accelerates, the Hubble parameter is still decreasing. Confusing eh?
All the Hubble constant represents is
the average of the rate at which the universe has expanded over the age of the universe. It represents how much the universe would have had to expanded, over the past 13.7 billion years, for it to reach the size it is today. It would have had to have expanded at an average of around 70km/s/Mpc to do so.
The thing to remember is that when cosmologists talk of constant expansion, it means that objects recede at a constant speed, and that speed increases with distance. The further away something is, the faster it recedes, and it continues to recede at that speed. More distant objects will recede at a faster but constant speed and closer objects will recede with a slower but constant speed.
Objects only accelerate away from us in an accelerating universe (in a universe with no cosmological constant, only gravity, what is there that would make an object accelerate away from us?), and only in an accelerating universe is there a cosmic event horizon which objects pass beyond and become invisible. That horizon is not where the object recedes at the speed of light (known as the Hubble distance), it is the distance beyond that where the light from a distant event cannot make it to our Hubble distance, and it is known as the cosmological event horizon, or the light horizon.
We can see galaxies that are, and always have been, receding faster than light, but due to the acceleration of the rate of expansion there is a limit to how far past the Hubble distance we can see an event from.
The Hubble constant only actually remains constant during certain extreme forms of exponential expansion, like for instance the inflationary epoch or the ultimate fate of an accelerating universe.
I am not denying the "expansion of space" can make objects accelerate away from us, I am only denying that constant expansion (the state between deceleration and acceleration) does so.
Not such a quick question, this one.