The ANC clearly wants to get rid of Thabo Mbeki, but how will they go about doing it, there are a few options available to them, but what will it be, remember this is pure speculation on my part.
They can try to persuade Mbeki to resign, if he accepts, and resigns his position must be filled within thirty days by Parliament, by someone who is already a member of parliament - Baleka Mbete / Kgalema Mothlante - seem the likely choices, as the rest of the Zuma camp, including Zuma are not in Parliament
It is however, highly unlikely that Mbeki will step down, evident by the harsh statements made by cabinet that they do not agree with Judge Chris Nicholson's findings
The other way is by means of the constitution, in terms of section 89, a President may be removed if he violated the constitution or law, engaged in serious misconduct, or is unable to perform the functions of President, these would have to be proven - it will be difficult and extremely time consuming to try and prove any of these - and an attempt will most certainly fail.
Then there is section 102 - which allows for a vote of no confidence in the President, this merely requires a two-thirds majority vote in Parliament, in which case the President, his cabinet and deputy ministers must resign.
Parliament then has thirty days to elect a President, who will then appoint Ministers and Deputy Ministers - again from within parliament. This will see the complete halt of government and could lead to chaos - not a rout I believe the ANC would consider. Also they have to be sure they have the parliamentary majority to pull the motion off, and then the right people in parliament to appoint to Government - remember the leading figures in the Zuma camp are not in parliament - if it is not done within thirty days, Parliament is dissolved and elections must be held.
The only other way is to call for an early election, the ANC is not keen on this as they need time to prepare and campaign - they have already released their campaign strategy, in any event, the IEC needs at least 90 days notice to hold elections - not to mention court challenges from other parties who may not be ready to run an election.
I am not sure what the ANC is going to do, but I figure that they will in all probability, come out of the NEC meeting and say something like, while we agree with the findings and inferences made by Judge Chris Nicholson, the NEC of teh ANC feels it would be premature to act on those findings while the NPA is appealing the decision, we will therefore wait for a further ruling by the appeal court, before making any further decisions on the matter.
This will give them time to try to unite the party, and win back disillusioned Mbeki supporters, remember Zuma was elected in Polokwane, but not by an overwhelming majority, and the ANC would be cautious of losing those votes and teh two-thirds majority in Parliament