How far away are objects whose light will never reach us, because of the expansion of the universe? I thought I had read this question on Stack Exchange before, but now I cannot find it...   In fact, I thought I had posted this question before, somewhere, on Stack Exchange...
I believe the answer was about 62 billion light years...
In other words, if an object is currently 62 billion light years away, or more, the light it is emitting right now will never reach Earth...
Is there a term for this 'line' or 'sphere'?
There are several different quantities of this sort that you can define, and the definitions are fairly confusing. Hopefully the following diagram will make things clearer.
                   Z                      &lt;- future infinity
                  / \
                 /   \
                /     \
      D   C    B   A   B    C   D         &lt;- now
      .   .   /   / \   \   .   .
      .   .  /   /   \   \  .   .
      .   . /   /     \   \ .   .
      .   ./   /       \   \.   .
      .   /   /         \   \   .
      .  /.  /           \  .\  .
      . / . /             \ . \ .
      ./  ./               \.  \.
~~~~~~d~~~c~~~~~~~~a~~~~~~~~c~~~d~~~~~~   &lt;- last scattering (universe opaque below this)

The horizontal axis on this diagram is &quot;comoving distance&quot;, with respect to which objects that move with the Hubble flow are at rest. The vertical axis is &quot;conformal time&quot;, with respect to which light travels along diagonal lines of a constant slope (in combination with the comoving distance).
A is our current location; Z is the ultimate location in the far future of the same matter, supposing it doesn't deviate much from the Hubble flow.
Light emitted in the current cosmological era from closer than B will reach us at some point in the future. Light emitted in the current era from farther than B will never reach us (if we don't deviate too far from the Hubble flow). The distance from A to B is around 16 Gly (billion light years). This seems like the closest match to the quantity you were asking about in your question. I'm not sure that it has a name.
Light emitted at the last scattering time from c is just reaching us now. This is the cosmic microwave background radiation. The distance in the present era from us to the presumed current location of the matter than emitted that light (if it hasn't deviated too much from the Hubble flow) is the distance from A to C. That distance is around 46 Gly. This is what's normally called the radius of the observable universe. Note that the distance from a to c is around 1100 times smaller, or 42 Mly.
Light emitted at the last scattering time from closer than d will eventually reach us. Light emitted at the last scattering time from farther than d never will (if we don't deviate from the Hubble flow). The present-day distance from A to D, which is the extrapolated current location of that matter supposing it doesn't deviate from the Hubble flow, is around 62 Gly. Again, the distance from a to d is around 1100 times smaller. (And the distance at future infinity is ∞ times larger.)
So your statement that &quot;if an object is currently 62 billion light years away, or more, the light it is emitting right now will never reach Earth&quot; is incorrect, but it would be correct if you replaced 62 by 16, or if you replaced &quot;is emitting right now&quot; by &quot;emitted at the last scattering time, supposing it didn't deviate too much from the Hubble flow&quot;. Also, you should probably replace &quot;Earth&quot; by &quot;whatever matter is left at Earth's location in the distant future, where 'location' is defined by the Hubble flow&quot;.