diff --git a/src/ol/Overlay.js b/src/ol/Overlay.js
index cfdc81b205..06f50a7c4a 100644
--- a/src/ol/Overlay.js
+++ b/src/ol/Overlay.js
@@ -249,14 +249,14 @@ class Overlay extends BaseObject {
 
   /**
    * Get the map associated with this overlay.
-   * @return {import("./PluggableMap.js").default|undefined} The map that the
+   * @return {import("./PluggableMap.js").default|null} The map that the
    * overlay is part of.
    * @observable
    * @api
    */
   getMap() {
-    return /** @type {import("./PluggableMap.js").default|undefined} */ (
-      this.get(Property.MAP)
+    return /** @type {import("./PluggableMap.js").default|null} */ (
+      this.get(Property.MAP) || null
     );
   }
 
@@ -378,8 +378,8 @@ class Overlay extends BaseObject {
 
   /**
    * Set the map to be associated with this overlay.
-   * @param {import("./PluggableMap.js").default|undefined} map The map that the
-   * overlay is part of.
+   * @param {import("./PluggableMap.js").default|null} map The map that the
+   * overlay is part of. Pass `null` to just remove the overlay from the current map.
    * @observable
    * @api
    */
diff --git a/src/ol/control/Control.js b/src/ol/control/Control.js
index b94f705b8d..2dde885ae8 100644
--- a/src/ol/control/Control.js
+++ b/src/ol/control/Control.js
@@ -69,7 +69,7 @@ class Control extends BaseObject {
 
     /**
      * @private
-     * @type {import("../PluggableMap.js").default}
+     * @type {import("../PluggableMap.js").default|null}
      */
     this.map_ = null;
 
@@ -98,7 +98,7 @@ class Control extends BaseObject {
 
   /**
    * Get the map associated with this control.
-   * @return {import("../PluggableMap.js").default|undefined} Map.
+   * @return {import("../PluggableMap.js").default|null} Map.
    * @api
    */
   getMap() {
@@ -107,9 +107,10 @@ class Control extends BaseObject {
 
   /**
    * Remove the control from its current map and attach it to the new map.
+   * Pass `null` to just remove the control from the current map.
    * Subclasses may set up event handlers to get notified about changes to
    * the map here.
-   * @param {import("../PluggableMap.js").default} [map] Map.
+   * @param {import("../PluggableMap.js").default|null} map Map.
    * @api
    */
   setMap(map) {
@@ -121,7 +122,7 @@ class Control extends BaseObject {
     }
     this.listenerKeys.length = 0;
     this.map_ = map;
-    if (this.map_) {
+    if (map) {
       const target = this.target_
         ? this.target_
         : map.getOverlayContainerStopEvent();
diff --git a/src/ol/control/FullScreen.js b/src/ol/control/FullScreen.js
index 429c1bfc90..2ed725b96c 100644
--- a/src/ol/control/FullScreen.js
+++ b/src/ol/control/FullScreen.js
@@ -281,9 +281,10 @@ class FullScreen extends Control {
 
   /**
    * Remove the control from its current map and attach it to the new map.
+   * Pass `null` to just remove the control from the current map.
    * Subclasses may set up event handlers to get notified about changes to
    * the map here.
-   * @param {import("../PluggableMap.js").default} map Map.
+   * @param {import("../PluggableMap.js").default|null} map Map.
    * @api
    */
   setMap(map) {
diff --git a/src/ol/control/MousePosition.js b/src/ol/control/MousePosition.js
index e95a4b3116..8568f55148 100644
--- a/src/ol/control/MousePosition.js
+++ b/src/ol/control/MousePosition.js
@@ -212,9 +212,10 @@ class MousePosition extends Control {
 
   /**
    * Remove the control from its current map and attach it to the new map.
+   * Pass `null` to just remove the control from the current map.
    * Subclasses may set up event handlers to get notified about changes to
    * the map here.
-   * @param {import("../PluggableMap.js").default} map Map.
+   * @param {import("../PluggableMap.js").default|null} map Map.
    * @api
    */
   setMap(map) {
diff --git a/src/ol/control/OverviewMap.js b/src/ol/control/OverviewMap.js
index 140c3afa5e..c127ffcd1c 100644
--- a/src/ol/control/OverviewMap.js
+++ b/src/ol/control/OverviewMap.js
@@ -267,9 +267,10 @@ class OverviewMap extends Control {
 
   /**
    * Remove the control from its current map and attach it to the new map.
+   * Pass `null` to just remove the control from the current map.
    * Subclasses may set up event handlers to get notified about changes to
    * the map here.
-   * @param {import("../PluggableMap.js").default} map Map.
+   * @param {import("../PluggableMap.js").default|null} map Map.
    * @api
    */
   setMap(map) {
diff --git a/src/ol/control/ZoomSlider.js b/src/ol/control/ZoomSlider.js
index 93ebc8c7c1..c86a58f9b5 100644
--- a/src/ol/control/ZoomSlider.js
+++ b/src/ol/control/ZoomSlider.js
@@ -161,9 +161,10 @@ class ZoomSlider extends Control {
 
   /**
    * Remove the control from its current map and attach it to the new map.
+   * Pass `null` to just remove the control from the current map.
    * Subclasses may set up event handlers to get notified about changes to
    * the map here.
-   * @param {import("../PluggableMap.js").default} map Map.
+   * @param {import("../PluggableMap.js").default|null} map Map.
    * @api
    */
   setMap(map) {
diff --git a/src/ol/layer/Layer.js b/src/ol/layer/Layer.js
index 0c55fdc460..d788f3e7ab 100644
--- a/src/ol/layer/Layer.js
+++ b/src/ol/layer/Layer.js
@@ -47,7 +47,7 @@ import {listen, unlistenByKey} from '../events.js';
  * @property {SourceType} [source] Source for this layer.  If not provided to the constructor,
  * the source can be set by calling {@link module:ol/layer/Layer~Layer#setSource layer.setSource(source)} after
  * construction.
- * @property {import("../PluggableMap.js").default} [map] Map.
+ * @property {import("../PluggableMap.js").default|null} [map] Map.
  * @property {RenderFunction} [render] Render function. Takes the frame state as input and is expected to return an
  * HTML element. Will overwrite the default rendering for the layer.
  * @property {Object<string, *>} [properties] Arbitrary observable properties. Can be accessed with `#get()` and `#set()`.
@@ -71,7 +71,7 @@ import {listen, unlistenByKey} from '../events.js';
 /**
  * @classdesc
  * Base class from which all layer types are derived. This should only be instantiated
- * in the case where a custom layer is be added to the map with a custom `render` function.
+ * in the case where a custom layer is added to the map with a custom `render` function.
  * Such a function can be specified in the `options` object, and is expected to return an HTML element.
  *
  * A visual representation of raster or vector map data.
@@ -268,7 +268,7 @@ class Layer extends BaseLayer {
 
   /**
    * For use inside the library only.
-   * @param {import("../PluggableMap.js").default} map Map.
+   * @param {import("../PluggableMap.js").default|null} map Map.
    */
   setMapInternal(map) {
     this.set(LayerProperty.MAP, map);
@@ -276,7 +276,7 @@ class Layer extends BaseLayer {
 
   /**
    * For use inside the library only.
-   * @return {import("../PluggableMap.js").default} Map.
+   * @return {import("../PluggableMap.js").default|null} Map.
    */
   getMapInternal() {
     return this.get(LayerProperty.MAP);
@@ -291,7 +291,7 @@ class Layer extends BaseLayer {
    *
    * To add the layer to a map and have it managed by the map, use
    * {@link module:ol/Map~Map#addLayer} instead.
-   * @param {import("../PluggableMap.js").default} map Map.
+   * @param {import("../PluggableMap.js").default|null} map Map.
    * @api
    */
   setMap(map) {
diff --git a/src/ol/render/Box.js b/src/ol/render/Box.js
index 4b09e98033..d09fb0b99f 100644
--- a/src/ol/render/Box.js
+++ b/src/ol/render/Box.js
@@ -29,7 +29,7 @@ class RenderBox extends Disposable {
 
     /**
      * @private
-     * @type {import("../PluggableMap.js").default}
+     * @type {import("../PluggableMap.js").default|null}
      */
     this.map_ = null;
 
@@ -68,7 +68,7 @@ class RenderBox extends Disposable {
   }
 
   /**
-   * @param {import("../PluggableMap.js").default} map Map.
+   * @param {import("../PluggableMap.js").default|null} map Map.
    */
   setMap(map) {
     if (this.map_) {