Ongoing effects apply continuously during their duration. If they do not have a listed duration, they apply indefinitely while the source is in the realm. For example, King of the Realm's passive ability is an ongoing effect that gives you control of all mortals. Gnome Hollows' passive ability is an ongoing effect that prevents units with 3 or more power from entering. Quagmire's genesis ability creates an ongoing effect that causes units to be Immobile while they occupy nearby sites until your next turn. Between each event on the storyline, apply all ongoing effects. That is, the game is very regularly applying ongoing effects, both before and after each event on the storyline. Most of the time, the application of ongoing effects is straightforward; simply apply them. Complex interactions are described below.
If there are multiple ongoing effects, the game will apply all of them before checking to see if any minions died. For example, you have a Bosk Troll that has taken 1 damage this turn. Then, you move it to a location that is nearby both Wicked Witch and your House Arn Bannerman. Both the Witch and the Bannerman generate ongoing effects with their passive abilities. If the game applied the -2 power from the Witch first and then immediately checked for minions dying, the Bosk Troll would die, even though it shouldn't due to the House Arn Bannerman. Therefore, between each event on the storyline, the game applies all ongoing effects before checking for minions dying.
If ongoing effects overlap or conflict, apply them in the order listed here by layer: Copy effects, e.g. Mirror Realm, Selfsame Simulacrum Disabling effects, silencing effects, e.g. Root Spider, Iron Shackles, Silence, Sisters of Silence Control effects, e.g. King of the Realm, Mesmerism Type changing effects, e.g. Bower of Bliss, Corruptor Ability adding and removing effects, and affinity changing effects, e.g. Power of Flight, Watchtower, Tide Naiads, Drought Power setting effects, e.g. Shrink Power addition and subtraction effects, e.g. Overpower, Wicked Witch Power multiplication effects, e.g. Warp Spasm Within each layer, apply the effects based on their timestamp, from oldest to newest. For ongoing effects generated by a passive ability (e.g. King of the Realm, Root Spider), their timestamp is when the card entered the realm. For ongoing effects generated by an activated or triggered ability (e.g. Floodplain, Bog), their timestamp is when the ability was activated or triggered, not when the original source entered the realm. An effect cannot remove itself once it's already being applied. For example, an animated Silence aura will cause itself to lose its abilities in layer 2, but losing that ability will not remove the silence effect, which was already being applied. In the unlikely event that two or more cards enter the realm simultaneously and they have passive abilities that may need to be ordered (e.g. my King of the Realm and yours, entering simultaneously via Boneyard), the active player's cards are considered to have entered first (in the order of their choosing, if they have more than one entering simultaneously).
If you play King of the Realm and then I play King of the Realm afterward, the game applies both control effects in layer 3. Since your King is older, the game starts with that effect. Your King gives you control of all mortals, including my King. Then, when the second King's ability is being applied, he's already controlled by you due to the first King's ability. Therefore, you control all mortals and the first King 'wins.'
If you play Smokestacks of Gnaak and then I play another Smokestacks of Gnaak nearby, the game tries to apply both lose-ability effects in layer 5. Since your Smokestacks are older, the game starts with that effect. Your Smokestacks causes my Smokestacks to lose its ability. Then, when my Smokestacks ability would be applied, it already lost its ability due to the first Smokestacks. Therefore, the first Smokestacks 'wins.'
If you play Flood and then I play Drought, the game tries to apply both affinity changing effects in layer 5. Since you played Flood first, the game first gives the affected sites a minimum of one water affinity (W). Then, when my Drought ability is applied, the affected sites have no water affinity. Therefore, the Drought 'wins.' If Flood had been played second, then the Flood effect would have been applied second, and thus would 'win.' Remember that if an activated or triggered ability creates an ongoing effect, the effect applies based on when the ability activated or triggered, not when the original source entered the realm. For example, Floodplain's activated ability would 'win' against a Drought even if the Floodplain entered the realm before Drought, as long as the Floodplain's activated ability was used after Drought.
This is a complicated concept, perhaps the most complicated in the whole codex! Be warned. Let's start with examples. I have Lucid Dreamers in the realm and cast a Bosk Troll to them, so my Troll gains voidwalk. Then, I cast Power of Flight on my Trolls. When applying those ongoing effects, I apply them in layer 5. Technically, I apply the Voidwalk first (because it's older) and then I apply Airborne. But, the end result would be the same if I applied them in the opposite order; either way, I end up with a Troll that has Voidwalk and Airborne. These two ongoing effects do not depend on each other. Now, let's consider two Sisters of Silence. I play Sister A then you play Sister B nearby. We apply the silenced effect in layer 2. Since Sister A is older, the game applies that first, Sister B loses her ability, and Sister A retains her ability. If I applied them in the opposite order, Sister A would lose her ability and Sister B would retain hers. In this case, both ongoing effects depend on each other. Finally, let's consider one Sister of Silence and a Grievous Insult. I play my Sister of Silence and then you play Grievous Insult. Let's say you have a House Arn Bannerman nearby my Sisters. If we apply the Sisters first (because they entered the realm before the Grievous Insult was played), House Arn Bannerman will be silenced, and then the Sisters would be silenced by the Insult. In this scenario, the House Arn Bannerman would already be silenced and not get his ability back when the Sisters became silenced by the Insult! If we consider the alternate order, applying the Insult first, the Sisters still end up silenced, but the House Arn Bannerman will not be silenced. In this case, the Sisters' ability is dependent on the Insult, but the Insult is not dependent on the Sisters (since the Sisters end up Silenced by the Insult regardless of order). Player intuition would say that if I play Sisters and then you play Grievous Insult, we would expect the Grievous Insult to actually apply first, even though it was played later. That is the whole point of the dependency rule! If one effect depends on another (but not visa versa!), apply the independent effect first, ignoring normal timestamp order. This whole rule can probably be boiled down to 'use your intuition on how it should work.' Here are further examples: I play King of the Realm, and then you use Mesmerism my King of the Realm. Without the dependency rule, we would apply the control effect from my King of the Realm to all Mortals, then you would get control of only my King of the Realm via Mesmerism (but not all the other Mortals, because we already applied that effect). But that's obviously not the way it should work, since Mesmerism is independent of the King's effect. Therefore, we apply Mesmerism first, then King of the Realm. I play Fields of Phyxis to silence your Floodplain in front of it. Then, you play Acid Rain just on my Fields. If we applied these in order, my Fields would silence your Floodplain, then your Acid Rain would silence my Fields (but the Floodplain would already be silenced). But that's obviously not how it should work, since Acid Rain is independent of Fields. Therefore, we apply Acid Rain first, silencing Fields of Phyxis (and the Floodplains won't get silenced by the Fields). If there are multiple independent and dependent effects, apply the independent effects in timestamp order, then the dependent effects in timestamp order. For example, if I play King of the Realm, then you play King of the Realm, you Mesmerize my King, then I Infiltrate my King back... We would note that Mesmerize and Infiltrate are independent of the King's effects, and apply those first. Mesmerize, then Infiltrate. Then we'd apply the King's abilities in order after that. Finally, note that if two effects are both dependent on each other, use timestamp normally. Examples of that are detailed above in 'Example - Two Kings of the Realm,' 'Example - Two Smokestacks of Gnaak, and 'Example - Flood vs. Drought.'