Activation Tracing Rules
Activation tracing rules are similar to the Supply Tracing rules, except that the only geographic consideration is the range limitation of the HQ. Activation paths can cross unplayable Ocean hexsides and do not need to exit/enter ports to combine tracing over sea and land. Activation paths are blocked by the presence of enemy units/ZoI in the same way as supply paths are blocked.

Example 4:In the above picture, the Allies want to activate the British 16th Corps and Indian 1st Corps. A supply line to either unit from SEAC is blocked: the Japanese 17th Army is blocking the land route and because Japan controls Rangoon, supply by sea from Calcutta through Rangoon is not possible. However, the HUMP is active and because Dacca is a supply eligible airfield (it can trace a supply line to an ultimate supply source), Kunming can provide supply to the British 16th and Indian 1st Corps (black lines).
With both units in supply, SEAC only has to trace an activation path which is possible because unlike supply paths, the activation path does not need to enter a land mass from sea via a port to be traced overland. The SEAC air unit neutralizes the Japanese air unit's ZoI along the part of the activation path that goes by sea and once the path reaches land it can be traced to both the British 16th and Indian 1st Corps (red line). If the Japanese take Dacca, then the Allied supply position in Burma will collapse because the Allies will not have a supply eligible airfield to make Kunming a supply source. And without supply the Allied units in Burma will not be able to move.

Example 5:In the picture to the right, the Enterprise carrier stages off the cost of New Guniea during an offensive to launch an attack on Cairns. During reaction movement, the Japanese units in Cairns have an activation path from the SS HQ in Truk that avoids the unneutralized ZoI of the Enterprise. However, the supply line to Cairns is blocked at either Port Moresby or Gili-Gili by the Enterprise's ZoI. Unless supplied by another HQ, Japanese units in Cairns are not eligible to activate because they are out of supply.
Attrition and Reaction Tracing Rules
A ground or air unit that is reduced and out of supply must trace an Attrition path to an HQ. This path ignores geographic considerations as well as the presence of enemy units--the only limitation is the range of the HQ. Such units that are out of range are eliminated.
For example, on Turn 2, Japan captures Midway with 18-12 Army unit. During Attrition, the 18-12 will be out of supply because there are no Japanese HQs in range of Midway and will thus flip to be a 9-12 reduced Army. If the US had attacked Midway and flipped the 18-12 during the turn, then the reduced 9-12 would be out of supply and out of attrition range and would thus be eliminated during the Attirtion phase. (See 16.42 for why the difference between these two outcomes is significant.)
In order for an HQ to activate for Reaction movement, it must be in range of at least one battle hex. This range is "as the crow flies" and is limited only by the HQ's range.

Example 6: The above picture shows at a high level an Allied offensive into the DEI (units have been removed to better highlight the relevant HQ ranges). The Allies launch two attacks with units in or around Darwin. A smothering attack is made on Saigon to suppress a possible reaction amphibious assault by a Japanese 9-12 Army unit stacked there. The main attack is the invasion of Soerabja. The Allies expect the S HQ to react but since the Saigon battle is in range of the Combined Fleet HQ in Kure, the Japanese use this HQ to make reaction movement. Elite Japanese air and naval units currently stationed in the Central Pacific are activated by the Combined Fleet HQ and have the range to reach the battle in Soerabaja. Even though the battle hex in Soerabaja is not in range of the Combined Fleet HQ, all the units activated by the Combined Fleet HQ can join the battle in Soerabaja provided they can reach the battle hex.