Drupal 8.0.0 beta 12. More info: https://www.drupal.org/node/2514176

core/profiles/minimal/config/install/block.block.stark_admin.yml

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+id: stark_admin
+theme: stark
+weight: 1
+status: true
+langcode: en
+region: sidebar_first
+plugin: 'system_menu_block:admin'
+settings:
+  label: Administration
+  provider: system
+  label_display: visible
+  level: 1
+  depth: 0
+dependencies:
+  config:
+    - system.menu.admin
+  module:
+    - system
+  theme:
+    - stark
+visibility: {  }

core/profiles/minimal/config/install/block.block.stark_login.yml

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+id: stark_login
+theme: stark
+weight: 0
+status: true
+langcode: en
+region: sidebar_first
+plugin: user_login_block
+settings:
+  label: 'User login'
+  provider: user
+  label_display: visible
+dependencies:
+  module:
+    - user
+  theme:
+    - stark
+visibility: {  }

core/profiles/minimal/config/install/block.block.stark_messages.yml

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+id: stark_messages
+theme: stark
+weight: 0
+status: true
+langcode: en
+region: highlighted
+plugin: system_messages_block
+settings:
+  id: system_messages_block
+  label: 'Status messages'
+  provider: system
+  label_display: '0'
+dependencies:
+  module:
+    - system
+  theme:
+    - stark

core/profiles/minimal/config/install/block.block.stark_tools.yml

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+id: stark_tools
+theme: stark
+weight: 0
+status: true
+langcode: en
+region: sidebar_first
+plugin: 'system_menu_block:tools'
+settings:
+  label: Tools
+  provider: system
+  label_display: visible
+  level: 1
+  depth: 0
+dependencies:
+  config:
+    - system.menu.tools
+  module:
+    - system
+  theme:
+    - stark
+visibility: {  }

core/profiles/minimal/minimal.info.yml

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+name: Minimal
+type: profile
+description: 'Build a custom site without pre-configured functionality. Suitable for advanced users.'
+version: VERSION
+core: 8.x
+dependencies:
+  - node
+  - block
+  - dblog
+  - page_cache
+themes:
+  - stark

core/profiles/minimal/minimal.install

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+<?php
+/**
+ * @file
+ * Install, update and uninstall functions for the minimal installation profile.
+ */
+
+/**
+ * Implements hook_install().
+ *
+ * Performs actions to set up the site for this profile.
+ *
+ * @see system_install()
+ */
+function minimal_install() {
+  // Disable the user pictures on nodes.
+  \Drupal::configFactory()->getEditable('system.theme.global')->set('features.node_user_picture', FALSE)->save(TRUE);
+
+  // Allow visitor account creation, but with administrative approval.
+  \Drupal::configFactory()->getEditable('user.settings')->set('register', USER_REGISTER_VISITORS_ADMINISTRATIVE_APPROVAL)->save(TRUE);
+}

core/profiles/minimal/src/Tests/MinimalTest.php

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+<?php
+
+/**
+ * @file
+ * Contains \Drupal\minimal\Tests\MinimalTest.
+ */
+
+namespace Drupal\minimal\Tests;
+
+use Drupal\simpletest\WebTestBase;
+
+/**
+ * Tests Minimal installation profile expectations.
+ *
+ * @group minimal
+ */
+class MinimalTest extends WebTestBase {
+
+  protected $profile = 'minimal';
+
+  /**
+   * Tests Minimal installation profile.
+   */
+  function testMinimal() {
+    $this->drupalGet('');
+    // Check the login block is present.
+    $this->assertLink(t('Create new account'));
+    $this->assertResponse(200);
+
+    // Create a user to test tools and navigation blocks for logged in users
+    // with appropriate permissions.
+    $user = $this->drupalCreateUser(array('access administration pages', 'administer content types'));
+    $this->drupalLogin($user);
+    $this->drupalGet('');
+    $this->assertText(t('Tools'));
+    $this->assertText(t('Administration'));
+  }
+}