[BetterBatteryStats] :
Ok so after about 4h20min here are the results:

During the time the phone was for sure >95% of time just leaved alone. Configurations during test were:

wifi OFF

bluetooth OFF

gps OFF

flight mode OFF

phone mode ON

data network ON

auto rotate ON

sound ON

vibration ON

none of the apps beside BBS and settings->about phone->status were opened by me

===================
General Information
===================
BetterBatteryStats version: 1.4.2.0
Creation Date: 2011-12-24 13:54:08
Statistic Type: (0) Since Charged
Since 4 h 24 m 3 s
VERSION.RELEASE: 2.3.6
BRAND: samsung
DEVICE: GT-I9003
MANUFACTURER: samsung
MODEL: GT-I9003
===========
Other Usage
===========
Awake (): 9 m 11 s (551 s) Ratio: 3,5%
Screen On (): 6 m 54 s (414 s) Ratio: 2,6%
=========
Wakelocks
=========
sleep_broadcast (System Android): 30 m 58 s (1858 s) Count:42 11,7%
RILJ (Ekran wybierania): 57 s (57 s) Count:110 0,4%
ActivityManager-Launch (System Android): 27 s (27 s) Count:153 0,2%
GpsLocationProvider (System Android): 6 s (6 s) Count:17 0,0%
StartingAlertService (com.android.mms.Wiadomości): 3 s (3 s) Count:6 0,0%
SMSDispatcher (Ekran wybierania): 3 s (3 s) Count:1 0,0%
Checkin Service (Usługi Google): 3 s (3 s) Count:111 0,0%
AlarmManager (System Android): 2 s (2 s) Count:223 0,0%
show keyguard (System Android): 2 s (2 s) Count:55 0,0%
MediaScannerService (Multimedia): 2 s (2 s) Count:2 0,0%
*wifi* (System Android): 1 s (1 s) Count:43 0,0%
SCREEN_FROZEN (System Android): 1 s (1 s) Count:57 0,0%
Event Log Service (Usługi Google): 1 s (1 s) Count:9 0,0%
================
Kernel Wakelocks
================
"samsung-battery" (): 1 m 29 s (89 s) Cnt:(c/wc/ec)39/1/39 0,6%
"PowerManagerService" (): 38 s (38 s) Cnt:(c/wc/ec)237/0/0 0,2%
"alarm" (): 23 s (23 s) Cnt:(c/wc/ec)62/36/0 0,1%
"svnet" (): 18 s (18 s) Cnt:(c/wc/ec)126/0/126 0,1%
"alarm_rtc" (): 16 s (16 s) Cnt:(c/wc/ec)20/0/3 0,1%
"radio-interface" (): 8 s (8 s) Cnt:(c/wc/ec)35/0/0 0,1%
"event2-1456" (): 7 s (7 s) Cnt:(c/wc/ec)34/2/0 0,0%
"KeyEvents" (): (0 s) Cnt:(c/wc/ec)3565/0/0 0,0%
"mmc_delayed_work" (): (0 s) Cnt:(c/wc/ec)1026/0/1 0,0%
"power-supply" (): (0 s) Cnt:(c/wc/ec)91/0/0 0,0%
"power-supply" (): (0 s) Cnt:(c/wc/ec)91/0/0 0,0%
"power-supply" (): (0 s) Cnt:(c/wc/ec)91/0/0 0,0%
=========
Processes
=========
suspend (0): Sys: 9 s (9 s) Us: (0 s) Starts: 0
com.asksven.betterbatterystats_xdaedition (com.asksven.betterbatterystats_xdaedition.BetterBatteryStats): Sys: (0 s) Us: 2 s (2 s) Starts: 1
com.android.settings (System Android): Sys: (0 s) Us: 1 s (1 s) Starts: 2
mediaserver (1013): Sys: (0 s) Us: (0 s) Starts: 0
========
Services
========
Active since: The time when the service was first made active, either by someone starting or binding to it.
Last activity: The time when there was last activity in the service (either explicit requests to start it or clients binding to it)
See h t t p://developer.android.com/reference/android/app/ActivityManager.RunningServiceInfo.h tml
com.android.vending (com.android.vending.util.AlarmService)
Active since: 38 s
Last activity: 38 s
Crash count:0
com.sec.android.providers.drm (com.sec.android.providers.drm.OmaDrmConfigService)
Active since: 36 s
Last activity: 36 s
Crash count:0
com.sec.android.app.sns (com.sec.android.app.sns.SnsService)
Active since: 37 s
Last activity: 37 s
Crash count:0
com.android.phone (com.samsung.sec.android.application.csc.CscUpdateService)
Active since: 41 s
Last activity: 41 s
Crash count:0
com.android.phone (com.android.stk.StkAppService)
Active since: 34 s
Last activity: 43 s
Crash count:0
com.google.process.gapps (com.google.android.location.NetworkLocationService)
Active since: 29 s
Last activity: 29 s
Crash count:0
system (com.google.android.backup.BackupTransportService)
Active since: 25 s
Last activity: 25 s
Crash count:0
system (com.android.internal.service.wallpaper.ImageWallpaper)
Active since: 26 s
Last activity: 26 s
Crash count:0
com.android.systemui (com.android.systemui.statusbar.StatusBarService)
Active since: 26 s
Last activity: 26 s
Crash count:0
com.android.phone (com.android.phone.BluetoothHeadsetService)
Active since: 25 s
Last activity: 31 s
Crash count:0
com.wssyncmldm (com.wssyncmldm.DMService)
Active since: 40 s
Last activity: 40 s
Crash count:0
com.sec.android.inputmethod.axt9 (com.sec.android.inputmethod.axt9.AxT9IME)
Active since: 26 s
Last activity: 27 s
Crash count:0
com.google.process.gapps (com.google.android.gsf.gtalkservice.service.GTalkService)
Active since: 56 s
Last activity: 7 m 31 s
Crash count:0

I am not sure if my number of posts is enough to attach the file here so I just paste the info above

CPUSpy issue was mentioned by me in earlier post

Additional info:

battery current state 87%

android power consumption menu:

android system 37%

display 25%

standby network 23%

android system 4%

dial screen 2%

strange android system is here twice?

I hope you will find were is the solution