I have a partial IRA conversion to ROTH IRA (in 2001) that consists of stocks. SInce then, my broker sold some of the stocks and purchased new ones. Can I recharacterize my conversion (based on the amount I converted) or do i have to recharacterize individualo stocks?
If I recharacterize this year (was last year's conversion), can I still make a new (another portion of my IRA) conversion this year, without messing up the other recharacterization? CAN I do all this with the same custodian, or am I better off shift the amount I want to convert to another custodian and then do the new conversion?
Thank you for any suggestions.

Recharacterizations are based upon value, not the identity of investments. It can get complicated. But basically, if the Roth account only contains assets from this conversion (meaning no other contribution or conversion was made to this account), then recharacterizing 100% of the current value will cancel the conversion.