Samsung Galaxy S3 — Galaxy S3 Intermittent Charging?

Something strange can happen with Galaxy S3 charging - I have 2 phones - GT-i9300, stock Android 4.3, not rooted. Sometimes there is intermittent slow charging or even discharging with phone powered off. To better understand what is going on I installed the Galaxy Charging Current app - this has proved useful to monitor the charging current (phone powered on). The original Samsung chargers are capable of a good charge current and poor leads or contacts can be detected by monitoring the current using the app.

I am confident that I have good chargers, leads, micro-USB sockets and batteries yet the S3 charge rate can be intermittently slow. Have tried new batteries and also a new Anker battery. The random problem appears to be within the S3. An odd thing is that if the charging current is found to be low, e.g. at 100mA, and the charger is switched off for say 10 seconds, then switched back on, the current can be very much higher and remain at or near this higher level (800-1000mA). If the current has later found to have dropped the procedure can be repeated - this effect is quite separate from the short-term high current immediately after connecting a charger.

Do we have any information how the charge current is controlled in the S3? Is a battery charge controller IC used (as might be expected?) and/or is there some software running while the phone is charging but powered off? Is there a 'best' app for monitoring S3 charging current? Any thoughts on what might be going on here?